Yesterday I posted a new In59seconds video on Youtube, describing research showing that one of the best ways of falling asleep is actually to stay awake….

However, I had no idea that exactly the same idea crops up in Mary Poppins, and predates the research by over 40 years…..

Ah, but you explain it in 59 seconds, while it takes Mary Poppins 1 minute and 43 seconds. By the way, the exact length of time the insomniacs in the test slept.

After a good night’s sleep (not together), having kept their eyes open to fight off insomnia, Bolt, Gay and Lewis-Francis race each other in a 100 meters race. All of them run at a constant speed throughout the race.

Bolt beats Gay by 20 meters. Gay beats Lewis-Francis by 20 meters.

assuming you mean that gay is 20m when bolt finishes, and lewis-francis is 20m back when gay finishes, then l-w is 36m back when bolt finishes.

Eddie. Again a post that is off topic. Why do you persist in doing this?

It would do us all a very great favour if you would kindly just p*ss off

“…do us all a great favour…”? Speak for yourself, Gabby. I enjoy Eddie’s off-topic posts — They are reminiscent of Richard’s weekly Friday puzzles, which I miss. So it wouldn’t do me a “great favour” if Eddie followed your unkind suggestion. If you don’t like them, don’t read them.

ctj is correct. if Bolt is 20 meters aheaf of Gay at the finish line, that means Gay’s speed is 80% of Bolt’s. Similarly, Lewis-Francis’ speed is 80% of Gay’s. 80% of 80% is 64%, which means Lewis Francis would be 36 (100 – 64) meters behind Bolt when Bolt finishes.

On that basis …..

The snow glows white on the mountain tonight
Not a footprint to be seen
A kingdom of isolation,
And it looks like I’m the queen.

The wind is howling like this swirling storm inside
Couldn’t keep it in, heaven knows I tried!

Don’t let them in, don’t let them see
Be the good girl you always have to be
Conceal, don’t feel, don’t let them know
Well, now they know!

Let it go, let it go
Can’t hold it back anymore
Let it go, let it go
Turn away and slam the door!

I don’t care
What they’re going to say
Let the storm rage on,
The cold never bothered me anyway!

It’s funny how some distance
Makes everything seem small
And the fears that once controlled me
Can’t get to me at all!

It’s time to see what I can do
To test the limits and break through
No right, no wrong, no rules for me I’m free!

Let it go, let it go
I am one with the wind and sky
Let it go, let it go
You’ll never see me cry!

Here I stand
And here I’ll stay
Let the storm rage on!

My power flurries through the air into the ground
My soul is spiraling in frozen fractals all around
And one thought crystallizes like an icy blast
I’m never going back,
The past is in the past!

Let it go, let it go
And I’ll rise like the break of dawn
Let it go, let it go
That perfect girl is gone!

Here I stand
In the light of day
Let the storm rage on,
The cold never bothered me anyway!

It certainly does look like you’re the queen.

@Edie You have not responded to your own Puzzle of March 6, 2015.

I think perhaps this is because you yourself do not know the Solution.

This is nothing to be especially ashamed of. Not all of us know the answers to the truly meaningful questions of life – such as why we exist and what our purposes is – so to not know the answer to a simple puzzle is in some ways a preparation for that sense of wonder that will come when we are mature enough to tackle the truly meaningful questions.

Yet it may by some be considered disrespectful to misrepresent you yourself as a Puzzle Setter when you lack the commitment to follow through on that for which you have promised to deliver – i.e. a Solution.

You may at this point be feeling as others will that you need a personal coach to help you establish your life goals and to gently encourage you to greater efforts when ofttimes you fall short.

I am humbly offering to take on such a role with you. It may be a long and arduous personal journey for you yet the quickest way to complete it is to take that first step. Please join me in helping you to excel.

Is it that each row and column is comprised solely of the five digits 1,2,2,5, and 8? Too bad the diagonals don’t follow the same rule–that would truly be magical.

If you subtract 1 from each of your nine numbers then the “magic” constant becomes 42.

I place “magic” in quotes as there is no real magic in numbers. There are it is true mystic numbers but not as many as many people – even scientists – think there are.

42 has achieved near mystic status as it is strongly associated with an aspiration to attain the “answer to life and the universe” as originally popularised by Dougal Adams in his Hitchers Guide to the Galaxy.

Whether 42 has any true mystic significance has been greatly debated and ofttimes even astrologers have been asked for opinion on the Question.

Yet this is not an issue we can readily rule upon – despite it being flattering to have been asked.

Humans and numbers have an intimate connection. As do numbers and the true mathematical truths of the universe. Thus indeed by simple correlation humans have a connection to the truths of the universe.

Yet is is not as simple as claiming an emotional resonance with a number as having a wider significance. We aspiring mystics must always retain a down-to-earth scepticism that enables us to truly assess and analyse such claims rather than to state them as true simply because we would like them to be so.

Thus as stated: 42 is not a magic number despite it being claimed as such in the “magic square – 1” that Edie has presented to us.

We should be wary of Edie’s claims to know of magic. He may indeed be a fledgling magician. Yet also too he may be a trickster sent to swerve us from the path of truth into some darker distraction.

Magic – true magic – is not to be trifled with.

You should all be aware by now of the corny kind of puzzle I usually set.

Anyway, good effort Ken, but the answer lies in the number of letters in each number (spelt out). When done, this set also forms a magic square summing to 21 on each line, which admittedly is half of 42.

Barry, you went off on a tangent as usual.

That was me and the puzzle is actually one of Martin Gardner’s.

Hi Barry Goddard.

I don’t think the ‘Magic’ in ‘Magic Square’ literally pertains to ‘Magic’. I think it is just intended as a quirky epithet. The thing about non-mystics, is that they know and love a metaphor when they see one. Hope that clears up the issue a little for you.

Thanks.

Allow me to briefly explain. This is a curious arrangement of numbers includes what is referred to as a “magic square”.

The magic derives from the fact that numbers arranged in a square of equal sides all add to the same total, coming and going, up and down, and oft times even from an angle (diagonal). For example:

6 1 8

7 5 3

2 9 4

Note that the total always adds to 15 (row, column or diagonal), the diagonals no longer necessarily add properly if either the row and/or columns are mixed, and the total of any three rows or columns is 45. This is a magic square of rank 3.

More information on this topic can be found at the Halexandria Forums.
One can also do a 4×4 magic square, e.g.

1 16 12 5

15 2 13 4

8 9 6 11

10 7 3 14

Here the rows and columns add to 34, but in this particular case the diagonals do not.

The 3×3 example above is considered Panmagic, Diabolical, Nasik, or Pandiagonal, while the 4×4 above is merely magic.

It is also possible to start with zero, instead of one, so that a possible 5×5 magic square is:

21 2 8 14 15

13 19 20 1 7

0 6 12 18 24

17 23 4 5 11

9 10 16 22 3

This particular version was taken from , which is an excellent website on the subject. Included is a very brief, traditional history, which notes that “all magic squares have at least eight variations: the square can be rotated into four positions and each of these rotations can be reflected – for a total of eight variations of any one unique design. Most magic squares do not remain magic if one border is moved to the opposite edge – the change leaves the main diagonal no longer magic. However, translocation – repeatedly moving one edge across to the opposite side or the top to the bottom – does not affect panmagic squares which have, therefore, additional variations.

“In a 5 x 5 square this is equivalent to moving the starting square through all twenty-five positions – for a total of 25 x 8 = 200 variations. For the order 7 square, each pan-magic square has 49 x 8 = 392 variations and for the size 11 square there are 121 x 8 = 968 variations.” He also notes that, according to his book on Magic Squares and Cubes, William Andrews describes the construction of panmagic squares of order 5, and predicts that the total number of possible panmagic squares of order five will be 28,800.”

The 6×6 magic square is particularly interesting. Two examples include:

6 32 3 34 35 1 32 29 4 1 24 21

7 11 27 28 8 30 30 31 2 3 22 23

24 14 16 15 23 19 12 9 17 20 28 25

13 20 22 21 17 18 10 11 18 19 26 27

25 29 10 9 26 12 13 16 36 33 5 8

36 5 33 4 2 31 14 15 34 35 6 7

Here, every number between 1 and 36 is used. All columns and rows (and the two diagonals) add to 111. The total of all rows (or all columns) is thus “666”! Which also says that 1+2+3+…+36 = 666! Note also that shifting the columns eliminates the fact that each of the diagonals add to 111.

An intriguing aspect of the 6×6 magic square on the right is that if one looks at adjacent numbers, one obtains a pattern of the sequence of numbers in the 2×2 squares:

X X X

X U X

U X U

Such patterns are common in many magic squares, particularly when one uses formulas to derive the sequence of numbers.

(9/22/9) Even more astounding in some respects is a three-dimensional magic… double tetrahedron (or star tetrahedron). See, for example, the forum thread on 09/09/09.

Magic?

If Magic is nothing more than our current understanding of technology and science, then Magic Squares may indeed be magic. There may be a hidden science of which we are blissfully unaware which magic squares describe, even when the mathematicians have exhaustively delved into the subject, thinking of it as no more than a mental exercise. We may have become adept at manipulating magic squares and constructing them, but are they actually understood? Probably not.

By the same token, is it possible that there is really no profound hidden meaning to begin with? Of course. But as in Sacred Geometry, where we begin to see Philosophy as a mathematical discipline, then Magic Squares may have their own hidden values as well.

One might notice, for example, that the total of the 6×6 magic square is 666, the so-called number of the beast. It should be pointed out, however, that “666” shows up twice in the Bible, once in Revelation 13:18, but also earlier in King Solomon’s time [1 Kings 10:14]. In both cases, the phraseology is: “six hundred threescore and six”; e.g.:

Revelation 13:18: “Here is the wisdom. Let him that hath understanding count the number of the beast: for it is the number of a man; and his number is Six hundred threescore and six.”

1 Kings 10:14: “Now the weight of gold that came to Solomon in one year was six hundred threescore and six talents of gold.”
The degree of magic in a magic square might also be hinted at from its history. In another excellent website, , the author notes that, “Magic squares have been around for over 3,000 years. They are descendants of the oldest known number mystery, the legend of Lo Shu, found in China in a book entitled Yih King.”

The story of Lo Shu is basically one of a huge flood in ancient China, whereby sacrifices to the river god — to calm his anger — seem ineffective. Each time a turtle came out of the river and walked around the sacrifice, as if to suggest that the river god had not accepted the sacrifice. Until a child noticed a curious figure on the turtle shell — in effect, the 3×3 magic square shown above. On this basis, the people realized the correct amount of sacrifice to make, and thus appeased the river god.

Apparently, these ancient Chinese believed in the magic!

In 1514, Albrecht Dürer created an engraving named Melancholia that included a magic square. In the bottom row of his 4×4 magic square, he placed the numbers “15” and “14” side by side to reveal the date of his engraving.

16 3 2 13

5 10 11 8

9 6 7 12

4 15 14 1

Possibly the premier website on the subject, complete with lots of math and an excellent bibliography is . This website notes, among many, many other aspects, that, “Various numerological properties have also been associated with magic squares. Pivari associates the squares illustrated below with Saturn, Jupiter, Mars, the Sun, Venus, Mercury, and the Moon, respectively.”

4 9 2 4 14 15 1

3 5 7 9 7 6 12

8 1 6 5 11 10 8

16 2 3 13

Saturn = 15/45 Jupiter = 34/136

11 24 7 20 3 6 32 3 34 35 1

4 12 25 8 16 7 11 27 28 8 30

17 5 13 21 9 19 14 16 15 23 24

10 18 1 14 22 18 20 22 21 17 13

23 6 19 2 15 25 29 10 9 26 12

36 5 33 4 2 31

Mars = 65/325 Sun = 111/666

22 47 16 41 10 35 4 8 58 59 5 4 62 63 1

5 23 48 17 42 11 29 49 15 14 52 53 11 10 56

30 6 24 49 18 36 12 41 23 22 44 45 19 18 48

13 31 7 25 43 19 37 32 34 35 29 28 38 39 25

38 14 32 1 26 44 20 40 26 27 37 36 30 31 33

21 39 8 33 2 27 45 17 47 46 20 21 43 42 24

46 15 40 9 34 3 28 9 55 54 12 13 51 50 16

64 2 3 61 60 6 7 57

Venus = 175/1225 Mercury = 260/2080

37 78 29 70 21 62 13 54 5

6 38 79 30 71 22 63 14 46

47 7 39 80 31 72 23 55 15

16 48 8 40 81 32 64 24 56

57 17 49 9 41 73 33 65 25

26 58 18 50 1 42 74 34 66

67 27 59 10 51 2 43 75 35

36 68 19 60 11 52 3 44 76

77 28 69 20 61 12 53 4 45

the Moon = 369/3321

The patterns in these squares formed from adjacent numbers are quite interesting. Note also, the sequence from Saturn to Jupiter and on to the Moon. In each case, the period of the cycles of each with respect to the Earth is decreasing — just as in the Days of the Week and their association with the planets.

Pivari, F. , has described briefly, the connection between these Magic Squares and Numerology, basing much of his material on the original writings of Cornelius Agrippa (1486-1535). Heinrich Cornelius Agrippa von Nettesheim was Counseller to Charles the Fifth, Emperor of Germany, and Iudge of the Prerogative Court, and was one of the more influential writers of renaissance esoterica. His de occulta philosophia in three books was considered a systematic exposition of various kinds of magic. Whether or not he had a clue about what he was writing is not immediately obvious, but one suspects there is some profound and practical stuff to be gleamed from his writings. For anyone brave enough to traverse through sixteenth century German, or seventeenth century English, link to .

The beginnings for example are:

“It is affirmed by Magicians, that there are certain tables of numbers distributed to the seven planets, which they call the sacred tables of the planets, endowed with many, and very great vertues of the Heavens, in as much as they represent that divine order of Celestiall numbers, impressed upon Celestials by the Idea’s of the divine mind, by means of the soul of the world, and the sweet harmony of those Celestiall rayes, signifying according to the proportion of effigies, supercelestiall Intelligencies, which can no other way be expressed, then by the marks of numbers, and Characters. For materiall numbers, and figures can do nothing in the mysteries of hid things, but representatively by formall numbers, and figures, as they are governed, and informed by intelligencies, and divine numerations, which unite the extreams of the matter, and spirit to the will of the elevated soul, receiving through great affection, by the Celestiall power of the operator, a power from God, applyed through the soul of the universe, and observations of Celestiall constellations, to a matter fit for a form, the mediums being disposed by the skill, and industry of Magicians; But let us hasten to explain the tables severally.”

If that is completely clear to you, then link to Agrippa and study it all. [And pay particular attention to pages 19 through 25 of Part 2 of Book II. Celestial Magic. Some of this is reproduced below for convenience.]

Meanwhile, we might note that in the 5×5, 7×7, and 9×9 magic squares, not only are the diagonal totals the same as the rows and columns, but the two diagonals at equal distances from the center diagonal add to the same total when divided by two. Furthermore, in the right-slanting diagonals, each of the adjacent numbers have a difference of exactly 5, 7, or 9 — depending on the magic square. [However, one may have to complete the cycle to note this. For example, in the 9×9 magic square, going from 78 to 6, involves a 78, 79, 80, 81, 1, 2, 3, 4, 5, 6 sequence — just as ten days from July 25 is August 4.] Adjacent numbers, and numbers with exact differences in sequence seem to be important.

We can look into the numbers associated with these seven magic squares by noting that:

Other variations on magic squares include Bimagic Squares (where replacing each number by its square in a magic square results in another magic square) and Border Squares. The latter represents the case where a magic square remains magic when its border is removed. An example is a 3×3 within a 5×5 within a 7×7, and is:

40 1 2 3 42 41 46

38 31 13 14 32 35 12

39 30 26 21 28 21 11

43 33 27 25 23 17 7

6 16 22 29 24 34 44

5 15 37 36 18 19 45

4 49 48 47 8 9 10

Note that in the above example that opposing border numbers always add to 50 (e.g. 38 + 12, 2 + 48, 13 + 37). This sum is the difference between the row totals of the 3×3 (75), and the 5×5 (125), and 7×7 (175).

Variations on magic squares can also be constructed using letters (either in defining the square or as entries in it), such as the alphamagic square and the Templar magic square. An alphamagic is “A magic square for which the number of letters in the word for each number generates another magic square. This definition depends, of course, on the language being used. In English, for example,

5 22 18 4 9 8

28 15 2 becomes 11 7 3

12 8 25 6 5 10

where the magic square on the right corresponds to the number of letters in

five twenty two eighteen

twenty eight fifteen two

twelve eight twenty five

The Templar Magic Square is a magic square-type arrangement of the words in the Latin sentence “Sator Arepo tenet opera rotas” (“the farmer Arepo keeps the world rolling”). This square has been found in excavations of ancient Pompeii.

S A T O R

A R E P O

T E N E T

O P E R A

R O T A S

Another version of this story, and referred to merely as the Sator Rotas magic square comes from , and notes that, “In Rome during the Middle Ages this square was inscribed on a variety of common, everyday objects such as utensils and drinking vessels. It was also found above doorways. It was believed that the square had magical properties, and that making it visible would ward off evil spirits. The words on this square roughly translate to ‘The Creator (or Savior) holds the working of the spheres in his hands.’”

Just read your answer, Eddie, about the number of letters in each number also forming a magic square. So cool! Just what I’d expect from Martin Gardner.

Thanks for that little bit of Culture DAve/Gabby.

Wow! If you add 100 to each number the MAGIC constant of 345 is achieved! 3, 4, 5. Get it?

OK, here’s one. Simplify the following algebraic expression in 26 variables (a thru z):
(x+a)(x-b)(x+c)(x-d)…(x-z).

oh I am sorry if you felt bad but I actually admired your research and reblogged only to show my admiration anyways this wont happen again.

These were my comments and opinions not Richards

ok right I didn’t notice that may be because it was my first comment on wordpress and I was too excited to get the reply I thought reblogging here is not a wise decision when u commented anyways do u still think reblogging here is equal to stealing??

What? You’re soliciting an opinion from this interloping fool? (See his other comments further up)

It’s not stealing. As long as you give acknowledgement to the original source then you are fine to do do. My apologies

Eddie. I refer you to the reply given in the case of “Arkell v. Pressdram”

ok thanks for the reply.

Re-blogging is fine as long as you cite the source. Despite what others say. 😛

@Anonymous

> Barry, you went off on a tangent as usual.

Thank you! That is high praise indeed.

To go on a tangent is to swing away from the narrow closed world of the circle. To go infinitely far outside the box – even if it be a circular box or “sphere” as some may call it – and to explore the deeper further reaches of the very universe itself.

It is to be one who does not go round and round in circles thinking the same tiny thoughts over and over again. Instead it is to be one who boldly explores the unreached depths of the perhaps imfathomable world we all form part of.

I am humbled by such praise from one who themselves is so modest as to draw a veil over their own name.

Thank you again @anonymous. You have true insight and the grace to offer praise where you see it. May all your secants be tangents.

What a pity that this “magic” is mere number twiddling.

I can see that mathematicians who are clearly jealous of the deeper skills of the magician may have over the centuries developed a deep seated envy.

Yet is is surely simply recognisably an example of professional misconduct to take a word as powerful and resonant as “magic” and use it to mean “adding up trick”.

I am disappointed yet somehow not surprised that mathematicians would stoop as low.

Tommy Cooper. A funny man but a seriously good magician too

Sorry about posting this but there’s not a lot else happening on here. What are the current ages of the following two people? Alan is twice as old as Bob was when Alan was as old as Bob is now.” Sum of their current ages is 49. Similtaneous equations may be required, but I prefer the graphical approach.

There’s a reason why people don’t come here any more! More fool me.
My head is hurting and I’m sorry but I had to do a worked example to understand what was going on, which then led to se’s (and then me kicking myself because I should have been able to do it in my head). Although I’m still having problems drawing it graphically.

Draw a graph: y axis = age, x axis = time. Draw the age timelines of the two men in the xy space and it becomes clear because the lines are parallel and with gradients 45 degrees.

Yeah, I’d got that (and the x+y = 49 line as well) although doing it on a post-it wasn’t the best foundation – it was translating the English into the distance between the parallel lines that was screwing my mind. A good question (rather like “this man’s father…” but to another level)

The first statement reduces to : A = 2(B – (A-B))
or (using the second statement)
49 – B = 4B – 2(49 – B)
49 – B = 6B – 98
7B = 147
B = 21
(using the second statement)
A = 49 – B = 28

I got it sorted by having A and B being the current ages and A-prime and B-prime for being their ages at the key point in the past. 4 unknowns, 4 equations, solved similtaneously, or at least, in order, took me to the answer. It is the magic of English that so few words which in themselves are so plain can lead to such stimulation of the mind, when they refer to the wonder of mathematics. And the fact that you can represent the solution graphically draws out further nuances of the topic.

Sorry, posted from different source then, so didn’t get my name picked up!

This was fun. Had to dissect the language to get it. First, I worked out the obvious unknowns: current ages (A and B), and their former ages (a and b). The “hidden” unknown is their age gap (x).

The givens were that A = 2b when a = B and that A + B = 49.

Of course, x = A – B = a – b; their age gaps being constant. I then saw that x is also B – b, their age gap being equal to the time lapse between a and A and b and B.

I then expressed A and B in terms of x and got that they were 4x and 3x, respectively.

I solved for x using A + B = 49 and got 7.

I got the same results as Gabby for the current ages but not as quickly.

Gabby Bollard, I admire how you quickly translated “Bob’s age when Alan was as old as Bob is now” to “B – (A – B)”. It would appear you immediately saw that their age gap is the same as the time lapsed.

Then again, English is not my first language. 😀

@Edie

A puzzle based on tricky “clever” wording is no puzzle at all. It simply is a word game. These can add nothing to the beauty of the human soul and as such can only be a distraction on our journey of discovery of the depths of human insight and compassion.

I ask you again simply as a favour to your own innate higher self to reflect at least twice before posting any more such frivolities.

You may wish to visit any number of websites devoted to the japanese zen art of the koan. These indeed are puzzles of the highest and most subtle nature often replaying years of gentle reflection and deep study. To truly solve a koan is to go beyond our limited self and to gain a glimpse of out limitless potential.

Please if you should post again in a few years may it be a koan you have truly solved. There then may be great rejoicings here rather than sad pencil scribblings as similtaneous equations are trotted once more out.

Please aspire to your higher self rather than to lower others.

Does your company do a self awareness and interpersonal skills training course?

That you for asking @edie. To humbly ask for assistance is to step onto the path to a solution. Many fail to take even such a first step.

Many courses and many approaches are possible. For best results all should be tailored to the student and at the same time allow the teacher’s strengths to shine forth.

Self-awareness and interpersonal skills are core abilities that I can teach and inspire with. I have many many years of active successful and practical experience in these areas.

You will know that from my contributions both here and elsewhere – such as my own blogs and tweets. The quality of my core work speaks not just for itself but to all who take a bare moment to evaluate it. Even those who initially are somewhat jaded and attempt to belittle my work are won over in time. You yourself may be an example of that.

So thus please ask what you wish and I will endeavor to assist you in all ways that I am capable of.

I would suggest that you have no self awareness or interpersonal skills because you talk over people and annoy intensely. In fact you sound quite aggressive the way you tout your quackery and force your opinions down people’s throats. I would never dream of asking you for assistance or taking your advice on any matter.

Barry Goddard

You are truly one of the most deluded and narcissistic people I have exchanged with on the internet. I know you are full of admiration for your own wisdom, self-awareness and interpersonal skills, but I can honestly say you have a unique ability to stir a negativity in me that I barely recognise. I know you take the unfalsifiable line that those that disagree with you are yet to see or accept your brilliance – and I might agree with you that my own uniquely negative reaction to your posts is my shortfall and not yours – but of course, that too is indistinguishable from narcissism. I am sorry if this comes across as one giant ad hominem, but I honestly think it would be useful for you to know that you come across the very opposite of the kind sage you think you are. I honestly hope this causes you to pause for thought, and allow a little more self-doubt into your life. My apologies if I have misjudged your situation, and there is something else going on that I have been insensitive to.

Nice try, Adzcliff. I think we now know we’re dealing with a psychopath here.

Thanks for this Eddie.

Personally though, I’m not sure he genuinely wishes anyone any ill-will (even if he does appear to look down his nose at his critics). I’m happy to give him the benefit of the doubt that he is just impressively narcissistic, with an impenetrable ego, and absolutely no self-awareness for how he comes across to those who question his self-professed brilliance. He strikes me as the sort of arrogant psychotherapist who would blame the patient for not getting better – or even worse, for their iatrogenia. It’s sort of fascinating in a way, but for some reason it annoys the hell out of me. I almost don’t recognise this reaction in myself? That’s not an emotional response you’d usually associate with a wise, self-aware, interpersonally-skilled teacher. I expect he thinks Socrates, Jesus and Galileo couldn’t please everyone. Anyway, this isn’t good for me…

@adzcliff

Thank you. I accept your apology for your having misjudged and you being insensitive.

It takes courage to admit that one is wrong – especially in such a public forum as an anonymous blog. That you can do so is a rare sign that there may be hope for your future spiritual development. For surely we all contain multitudes of potential once we just throw away the ego clinging that leads us to be judgmental and insensitive to others.

@Edie has decided to go it alone without my inestimable though humbly proffered help. This is of course entirely a personal decision and if it does not work out for the best I will always be there to re-offer my assistance once it can be seen to be needed. In the meanwhile @Edie please continue holding this thought in mind: “What would Barry Do?” It may help comfort you in troubled times.

That one apologies while one other turns their back is a “success” rate that is acceptable to me. I would like to use my skills and insight to help everyone. Yet I am no longer such a wide-eyed optimist to believe that is possible every single day. I will focus on those who request my contributions and look on with kindness on those who do not – even on those who forcibly reject my offers.

Peace and tranquility to us all. Even those who would hide from the world in puzzles and distraction.

A man decides to buy a nice horse. He pays $60 for it, and he is very content with the strong animal. After a year, the value of the horse has increased to $70 and he decides to sell the horse. However, already a few days later he regrets his decision to sell the beautiful horse, and he buys it again. Unfortunately, he has to pay $80 to get it back, so he loses $10. After another year of owning the horse, he finally decides to sell the horse for $90.

Consider the trade-story as if it describes two separate trades, where: In the first trade, the man buys something for $60 and sells it again for $70, so he makes a profit of $10.
In the second trade, the man buys something for $80 and sells it again for $90, so he makes again a profit of $10.

Conclusion: The man makes an overall profit of $10 + $10 = $20.

You can also look at the problem as follows: the total expenses are $60 + $80 = $140 and the total earnings are $70 + $90 = $160. The overall profit is therefore $160 – $140 = $20.

Well done. Where would we be without you (and your alter ego Barry)?

Yes. I am a Wise Man

Fascinating

@Edie

That is a fascinating story. Thank you for telling it.

I knew someone once who owned a sweet shop. They bought bars of chocolate wholesale at one price and sold them individually at another usually higher price. From this they made some money that helped pay the over heads on the building and so on. At the end of the whole process they sometimes made a profit.

Perhaps you could turn that into a grand opera. Singing “We have bought the chocolate. We have sold the chocolate. We have bought the chocolate. We have sold the chocolate” and so on. Repetitious “mantra” like chanting is key to operatic music and to much prayer and to much meditative practice.

Your repetitative story of a horse that was bought and sold and bought and sold falls squarely into that territory. Perhaps that should be set to music and staged and filmed by Steven Spielberg himself.

I am gently kidding you of course as you sometimes try to do with me. But I can see through your gruff exterior to the tiny child who is crying out for help. Perhaps your little pony was sold when you were young and this story of yours is all you have left of it.

May you find your true horse of infinite wisdom and may you not sell it for a minor profit before you have full use of it.

If you know any other stories of retail daring please do tell.

This is a most unusual paragraph. How quickly can you find out what is so unusual about it? It looks so ordinary that you would think that nothing is wrong with it at all, and, in fact, nothing is. But it is unusual. Why? If you study it and think about it, you may find out, but I am not going to assist you in any way. You must do it without any hints or coaching. No doubt, if you work at it for a bit, it will dawn on you. Who knows? Go to work and try your skill. Good luck!

For someone who wants me to stop posting these ‘off topic’ puzzles, you seem to display an inordinate enthusiasm for solving them.

I impressed myself with how quickly I got this. (I impress easy.) My next question was how long I would have to wait to show off, but then noticed I’ve been beaten to it…

I do not see what is so unusual about a sentence that has no letter E. Many words – perhaps the majority in English – have no letter E.

Your “unusual” sentence has no letter V or J or Z or X. Does that make it five times as unusual or does that made it quite usual indeed.

For those who wish to blight the blog with puzzles they should at least endeavour to get the rest of the blog community on there side by publishing puzzles that have been appropriately peer reviewed and are fair in the ways of solving.

To just publish something random because in your mind it is unusual is the worst form of journalism that leads us towards that perpertrated by the Daily Mail or the Guaridan.

None of us want puzzles when we could be having deeply enriching dialogue that shows us the way to emotional and intellectual liberation. Thus if puzzles are to be foisted on us please make them ones that are wholesome rather than full of holes.

I ask this as a humble representative of the silent majority on this website who have for too long watched the tiny minority enforce their will while pooh-poohing the rest of us for daring to have better and more grounded opinions that do not include a puzzle fixation.

In case you are confused: please do not confuse me with Gabby Bollard. I am not Ms Bollard. We have it is true similar names. Indeed I suspect Ms Bollard may be a pseudonym chosen to show an infatuation with myself.

Yet we have no connection with each other – other perhaps than subtle psychic resonances of which I will not speak at this time.

Ms Bollard has a certain agenda on this website – as indeed she is free to have and pursue. I have no such agenda other than to humbly assist the truth in any way that I can.

Therefore to consider that Ms Bollard is in some way an “alter ego” of mine is to fall into serious error that will prevent you seeing the true truth of the situation.

The internet is a place in which names can be fluid – and some take advantage of that. Yet still we must offer authentic communication else all is lost. I always strive to be authentic and humble and kind and helpful. These are the qualities by which you may recognise my postings even when others are trying poorly to make fun or play with names or just rightdown confuse us.

Could it be that I was born under the 13th sign, Ophiuchus?

Very few people know their true birth chart “star sign” as the process of assignment is far subtler and more thorough than your Daily Mail astrology columnist would have you believe.

As a long-time practitioner I would say focus less on your star sign and more on your inner potential. You need both of course as one is objective (the cosmos cannot lie) and one is inner subjective (thus easily misread and misunderstood).

Yet until you can safely and accurately read those inner intuitions without bias and filter you will not be able to read the objective truths written in the skies – you will just see additional subjective prejudices and wishful hopes and thinking.

Thus Gabby by all means have your birth chart read – I can offer such a service that is second to none in objective intuition – and use it as a starting point for your inner star trek.

Good to see you’ve given yourself a self-reassuring thumbs-up for you comment, Barry.

Molly has a set of four alphabet blocks. Each side of these blocks is printed with a different letter, making 24 in total. Molly notices that by rearranging the blocks, she can spell each of the following words:

Block 1: A, B, F, J, R, and S.
Block 2: D, E, L, U, W, and Y.
Block 3: C, I, M, N, O, and Z.
Block 4: G, H, K, P, T, and X.

From the word EXAM, we conclude that E and A are not on the same block.
From the word OGRE, we conclude that E and O are not on the same block.
From the word OKAY, we conclude that A and O are not on the same block.
Combining these, we conclude that A, E, and O are on different blocks. Assume that A is on block 1, E is on block 2, and O is on block 3.
From the words BOXY and EXAM, we conclude that X is not on the same block as A (block 1), E (block 2), and O (block 3), so X is on block 4.
From the words BOXY and OKAY, we conclude that Y is not on the same block as A (block 1), O (block 3), and X (block 4), so Y is on block 2.
From the word EXAM, we conclude that M is not on the same block as A (block 1), E (block 2), and X (block 4), so M is on block 3.
From the word OKAY, we conclude that K is not on the same block as A (block 1), Y (block 2), and O (block 3), so K is on block 4.
From the word BOXY, we conclude that B is not on the same block as Y (block 2), O (block 3), and X (block 4), so B is on block 1.
From the words BUCK and JUMP, we conclude that U is not on the same block as B (block 1), M (block 3), and K (block 4), so U is on block 2.
From the words PAWN and JUMP, we conclude that P is not on the same block as A (block 1), U (block 2), and M (block 3), so P is on block 4.
From the word JUMP, we conclude that J is not on the same block as U (block 2), M (block 3), and P (block 4), so J is on block 1.
From the words CHAW and BUCK, we conclude that C is not on the same block as A (block 1), U (block 2), and K (block 4), so C is on block 3.
From the words CHAW and PAWN, we conclude that W is not on the same block as A (block 1), C (block 3), and P (block 4), so W is on block 2.
From the word CHAW, we conclude that H is not on the same block as A (block 1), W (block 2), and C (block 3), so H is on block 4.
From the word PAWN, we conclude that N is not on the same block as A (block 1), W (block 2), and P (block 4), so N is on block 3.

Now, we must still have three letters for block 1, and two letters for each of the blocks 2, 3, and 4. We have the following letters left:

D, F, G, I, L, R, S, T, Z
From the words DIGS, FLIT and GIRL, we conclude that I is not on the same block as D, F, G, L, R, S, and T, so I is on the same block as Z. Furthermore, I and Z are on block 2, 3, or 4.
From the word ZEST, we conclude that Z is not on the same block as E (block 2), so Z is on block 3 or 4.
From the word OGRE, we conclude that G and R are not on the same block as E (block 2), and O (block 3), so G and R are on block 1 or 4, but not on the same block.
From the word GIRL, we conclude that I is not on the same block as G and R (block 1 or 4), so I is on block 2 or 3. Since Z is on block 3 or 4, I and Z must be on block 3. Now we have all six letters of block 3: C, I, M, N, O, and Z.

From the word GIRL, we conclude that L is not on the same block as G and R (block 1 and 4), so L is on block 2.
From the words FLIT and GIRL, we conclude that F, G, L, R, and T are not on the same block as L (block 2), and from the word ZEST, we conclude that S is not on the same block as E (block 2). So D must be on block 2.
Now we have all six letters of block 2: D, E, L, U, W, and Y.

From the words GIRL and DIGS, we conclude that G is not on the same block as R and S.
From the words FLIT and ZEST, we conclude that T is not on the same block as F and S.
Combining this, F, R, and S must be on the same block (block 1), and G and T must be on the same block (block 4).

Now we have all six letters of all blocks:
Block 1: A, B, F, J, R, and S.
Block 2: D, E, L, U, W, and Y.
Block 3: C, I, M, N, O, and Z.
Block 4: G, H, K, P, T, and X.

Ah, but you explain it in 59 seconds, while it takes Mary Poppins 1 minute and 43 seconds. By the way, the exact length of time the insomniacs in the test slept.

Yeah, but she was a lot better to look at. Made the time fly by.

Reblogged this on PeachQT and commented:

How to Fall Asleep

Aww, come on. Richard’s pretty good to look at.

After a good night’s sleep (not together), having kept their eyes open to fight off insomnia, Bolt, Gay and Lewis-Francis race each other in a 100 meters race. All of them run at a constant speed throughout the race.

Bolt beats Gay by 20 meters. Gay beats Lewis-Francis by 20 meters.

How many meters does Bolt beat Lewis-Francis by?

assuming you mean that gay is 20m when bolt finishes, and lewis-francis is 20m back when gay finishes, then l-w is 36m back when bolt finishes.

Eddie. Again a post that is off topic. Why do you persist in doing this?

It would do us all a very great favour if you would kindly just p*ss off

“…do us all a great favour…”? Speak for yourself, Gabby. I enjoy Eddie’s off-topic posts — They are reminiscent of Richard’s weekly Friday puzzles, which I miss. So it wouldn’t do me a “great favour” if Eddie followed your unkind suggestion. If you don’t like them, don’t read them.

ctj is correct. if Bolt is 20 meters aheaf of Gay at the finish line, that means Gay’s speed is 80% of Bolt’s. Similarly, Lewis-Francis’ speed is 80% of Gay’s. 80% of 80% is 64%, which means Lewis Francis would be 36 (100 – 64) meters behind Bolt when Bolt finishes.

On that basis …..

The snow glows white on the mountain tonight

Not a footprint to be seen

A kingdom of isolation,

And it looks like I’m the queen.

The wind is howling like this swirling storm inside

Couldn’t keep it in, heaven knows I tried!

Don’t let them in, don’t let them see

Be the good girl you always have to be

Conceal, don’t feel, don’t let them know

Well, now they know!

Let it go, let it go

Can’t hold it back anymore

Let it go, let it go

Turn away and slam the door!

I don’t care

What they’re going to say

Let the storm rage on,

The cold never bothered me anyway!

It’s funny how some distance

Makes everything seem small

And the fears that once controlled me

Can’t get to me at all!

It’s time to see what I can do

To test the limits and break through

No right, no wrong, no rules for me I’m free!

Let it go, let it go

I am one with the wind and sky

Let it go, let it go

You’ll never see me cry!

Here I stand

And here I’ll stay

Let the storm rage on!

My power flurries through the air into the ground

My soul is spiraling in frozen fractals all around

And one thought crystallizes like an icy blast

I’m never going back,

The past is in the past!

Let it go, let it go

And I’ll rise like the break of dawn

Let it go, let it go

That perfect girl is gone!

Here I stand

In the light of day

Let the storm rage on,

The cold never bothered me anyway!

It certainly does look like you’re the queen.

@Edie You have not responded to your own Puzzle of March 6, 2015.

I think perhaps this is because you yourself do not know the Solution.

This is nothing to be especially ashamed of. Not all of us know the answers to the truly meaningful questions of life – such as why we exist and what our purposes is – so to not know the answer to a simple puzzle is in some ways a preparation for that sense of wonder that will come when we are mature enough to tackle the truly meaningful questions.

Yet it may by some be considered disrespectful to misrepresent you yourself as a Puzzle Setter when you lack the commitment to follow through on that for which you have promised to deliver – i.e. a Solution.

You may at this point be feeling as others will that you need a personal coach to help you establish your life goals and to gently encourage you to greater efforts when ofttimes you fall short.

I am humbly offering to take on such a role with you. It may be a long and arduous personal journey for you yet the quickest way to complete it is to take that first step. Please join me in helping you to excel.

Zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz.

Please ignore the following if you are easily offended:

Consider the magic square below. Note that its rows, columns and diagonals each add up to the magic constant 45. What else about it is interesting?

5 22 18

28 15 2

12 8 25

Is it that each row and column is comprised solely of the five digits 1,2,2,5, and 8? Too bad the diagonals don’t follow the same rule–that would truly be magical.

If you subtract 1 from each of your nine numbers then the “magic” constant becomes 42.

I place “magic” in quotes as there is no real magic in numbers. There are it is true mystic numbers but not as many as many people – even scientists – think there are.

42 has achieved near mystic status as it is strongly associated with an aspiration to attain the “answer to life and the universe” as originally popularised by Dougal Adams in his Hitchers Guide to the Galaxy.

Whether 42 has any true mystic significance has been greatly debated and ofttimes even astrologers have been asked for opinion on the Question.

Yet this is not an issue we can readily rule upon – despite it being flattering to have been asked.

Humans and numbers have an intimate connection. As do numbers and the true mathematical truths of the universe. Thus indeed by simple correlation humans have a connection to the truths of the universe.

Yet is is not as simple as claiming an emotional resonance with a number as having a wider significance. We aspiring mystics must always retain a down-to-earth scepticism that enables us to truly assess and analyse such claims rather than to state them as true simply because we would like them to be so.

Thus as stated: 42 is not a magic number despite it being claimed as such in the “magic square – 1” that Edie has presented to us.

We should be wary of Edie’s claims to know of magic. He may indeed be a fledgling magician. Yet also too he may be a trickster sent to swerve us from the path of truth into some darker distraction.

Magic – true magic – is not to be trifled with.

You should all be aware by now of the corny kind of puzzle I usually set.

Anyway, good effort Ken, but the answer lies in the number of letters in each number (spelt out). When done, this set also forms a magic square summing to 21 on each line, which admittedly is half of 42.

Barry, you went off on a tangent as usual.

That was me and the puzzle is actually one of Martin Gardner’s.

Hi Barry Goddard.

I don’t think the ‘Magic’ in ‘Magic Square’ literally pertains to ‘Magic’. I think it is just intended as a quirky epithet. The thing about non-mystics, is that they know and love a metaphor when they see one. Hope that clears up the issue a little for you.

Thanks.

Allow me to briefly explain. This is a curious arrangement of numbers includes what is referred to as a “magic square”.

The magic derives from the fact that numbers arranged in a square of equal sides all add to the same total, coming and going, up and down, and oft times even from an angle (diagonal). For example:

6 1 8

7 5 3

2 9 4

Note that the total always adds to 15 (row, column or diagonal), the diagonals no longer necessarily add properly if either the row and/or columns are mixed, and the total of any three rows or columns is 45. This is a magic square of rank 3.

More information on this topic can be found at the Halexandria Forums.

One can also do a 4×4 magic square, e.g.

1 16 12 5

15 2 13 4

8 9 6 11

10 7 3 14

Here the rows and columns add to 34, but in this particular case the diagonals do not.

The 3×3 example above is considered Panmagic, Diabolical, Nasik, or Pandiagonal, while the 4×4 above is merely magic.

It is also possible to start with zero, instead of one, so that a possible 5×5 magic square is:

21 2 8 14 15

13 19 20 1 7

0 6 12 18 24

17 23 4 5 11

9 10 16 22 3

This particular version was taken from , which is an excellent website on the subject. Included is a very brief, traditional history, which notes that “all magic squares have at least eight variations: the square can be rotated into four positions and each of these rotations can be reflected – for a total of eight variations of any one unique design. Most magic squares do not remain magic if one border is moved to the opposite edge – the change leaves the main diagonal no longer magic. However, translocation – repeatedly moving one edge across to the opposite side or the top to the bottom – does not affect panmagic squares which have, therefore, additional variations.

“In a 5 x 5 square this is equivalent to moving the starting square through all twenty-five positions – for a total of 25 x 8 = 200 variations. For the order 7 square, each pan-magic square has 49 x 8 = 392 variations and for the size 11 square there are 121 x 8 = 968 variations.” He also notes that, according to his book on Magic Squares and Cubes, William Andrews describes the construction of panmagic squares of order 5, and predicts that the total number of possible panmagic squares of order five will be 28,800.”

The 6×6 magic square is particularly interesting. Two examples include:

6 32 3 34 35 1 32 29 4 1 24 21

7 11 27 28 8 30 30 31 2 3 22 23

24 14 16 15 23 19 12 9 17 20 28 25

13 20 22 21 17 18 10 11 18 19 26 27

25 29 10 9 26 12 13 16 36 33 5 8

36 5 33 4 2 31 14 15 34 35 6 7

Here, every number between 1 and 36 is used. All columns and rows (and the two diagonals) add to 111. The total of all rows (or all columns) is thus “666”! Which also says that 1+2+3+…+36 = 666! Note also that shifting the columns eliminates the fact that each of the diagonals add to 111.

An intriguing aspect of the 6×6 magic square on the right is that if one looks at adjacent numbers, one obtains a pattern of the sequence of numbers in the 2×2 squares:

X X X

X U X

U X U

Such patterns are common in many magic squares, particularly when one uses formulas to derive the sequence of numbers.

(9/22/9) Even more astounding in some respects is a three-dimensional magic… double tetrahedron (or star tetrahedron). See, for example, the forum thread on 09/09/09.

Magic?

If Magic is nothing more than our current understanding of technology and science, then Magic Squares may indeed be magic. There may be a hidden science of which we are blissfully unaware which magic squares describe, even when the mathematicians have exhaustively delved into the subject, thinking of it as no more than a mental exercise. We may have become adept at manipulating magic squares and constructing them, but are they actually understood? Probably not.

By the same token, is it possible that there is really no profound hidden meaning to begin with? Of course. But as in Sacred Geometry, where we begin to see Philosophy as a mathematical discipline, then Magic Squares may have their own hidden values as well.

One might notice, for example, that the total of the 6×6 magic square is 666, the so-called number of the beast. It should be pointed out, however, that “666” shows up twice in the Bible, once in Revelation 13:18, but also earlier in King Solomon’s time [1 Kings 10:14]. In both cases, the phraseology is: “six hundred threescore and six”; e.g.:

Revelation 13:18: “Here is the wisdom. Let him that hath understanding count the number of the beast: for it is the number of a man; and his number is Six hundred threescore and six.”

1 Kings 10:14: “Now the weight of gold that came to Solomon in one year was six hundred threescore and six talents of gold.”

The degree of magic in a magic square might also be hinted at from its history. In another excellent website, , the author notes that, “Magic squares have been around for over 3,000 years. They are descendants of the oldest known number mystery, the legend of Lo Shu, found in China in a book entitled Yih King.”

The story of Lo Shu is basically one of a huge flood in ancient China, whereby sacrifices to the river god — to calm his anger — seem ineffective. Each time a turtle came out of the river and walked around the sacrifice, as if to suggest that the river god had not accepted the sacrifice. Until a child noticed a curious figure on the turtle shell — in effect, the 3×3 magic square shown above. On this basis, the people realized the correct amount of sacrifice to make, and thus appeased the river god.

Apparently, these ancient Chinese believed in the magic!

In 1514, Albrecht Dürer created an engraving named Melancholia that included a magic square. In the bottom row of his 4×4 magic square, he placed the numbers “15” and “14” side by side to reveal the date of his engraving.

16 3 2 13

5 10 11 8

9 6 7 12

4 15 14 1

Possibly the premier website on the subject, complete with lots of math and an excellent bibliography is . This website notes, among many, many other aspects, that, “Various numerological properties have also been associated with magic squares. Pivari associates the squares illustrated below with Saturn, Jupiter, Mars, the Sun, Venus, Mercury, and the Moon, respectively.”

4 9 2 4 14 15 1

3 5 7 9 7 6 12

8 1 6 5 11 10 8

16 2 3 13

Saturn = 15/45 Jupiter = 34/136

11 24 7 20 3 6 32 3 34 35 1

4 12 25 8 16 7 11 27 28 8 30

17 5 13 21 9 19 14 16 15 23 24

10 18 1 14 22 18 20 22 21 17 13

23 6 19 2 15 25 29 10 9 26 12

36 5 33 4 2 31

Mars = 65/325 Sun = 111/666

22 47 16 41 10 35 4 8 58 59 5 4 62 63 1

5 23 48 17 42 11 29 49 15 14 52 53 11 10 56

30 6 24 49 18 36 12 41 23 22 44 45 19 18 48

13 31 7 25 43 19 37 32 34 35 29 28 38 39 25

38 14 32 1 26 44 20 40 26 27 37 36 30 31 33

21 39 8 33 2 27 45 17 47 46 20 21 43 42 24

46 15 40 9 34 3 28 9 55 54 12 13 51 50 16

64 2 3 61 60 6 7 57

Venus = 175/1225 Mercury = 260/2080

37 78 29 70 21 62 13 54 5

6 38 79 30 71 22 63 14 46

47 7 39 80 31 72 23 55 15

16 48 8 40 81 32 64 24 56

57 17 49 9 41 73 33 65 25

26 58 18 50 1 42 74 34 66

67 27 59 10 51 2 43 75 35

36 68 19 60 11 52 3 44 76

77 28 69 20 61 12 53 4 45

the Moon = 369/3321

The patterns in these squares formed from adjacent numbers are quite interesting. Note also, the sequence from Saturn to Jupiter and on to the Moon. In each case, the period of the cycles of each with respect to the Earth is decreasing — just as in the Days of the Week and their association with the planets.

Pivari, F. , has described briefly, the connection between these Magic Squares and Numerology, basing much of his material on the original writings of Cornelius Agrippa (1486-1535). Heinrich Cornelius Agrippa von Nettesheim was Counseller to Charles the Fifth, Emperor of Germany, and Iudge of the Prerogative Court, and was one of the more influential writers of renaissance esoterica. His de occulta philosophia in three books was considered a systematic exposition of various kinds of magic. Whether or not he had a clue about what he was writing is not immediately obvious, but one suspects there is some profound and practical stuff to be gleamed from his writings. For anyone brave enough to traverse through sixteenth century German, or seventeenth century English, link to .

The beginnings for example are:

“It is affirmed by Magicians, that there are certain tables of numbers distributed to the seven planets, which they call the sacred tables of the planets, endowed with many, and very great vertues of the Heavens, in as much as they represent that divine order of Celestiall numbers, impressed upon Celestials by the Idea’s of the divine mind, by means of the soul of the world, and the sweet harmony of those Celestiall rayes, signifying according to the proportion of effigies, supercelestiall Intelligencies, which can no other way be expressed, then by the marks of numbers, and Characters. For materiall numbers, and figures can do nothing in the mysteries of hid things, but representatively by formall numbers, and figures, as they are governed, and informed by intelligencies, and divine numerations, which unite the extreams of the matter, and spirit to the will of the elevated soul, receiving through great affection, by the Celestiall power of the operator, a power from God, applyed through the soul of the universe, and observations of Celestiall constellations, to a matter fit for a form, the mediums being disposed by the skill, and industry of Magicians; But let us hasten to explain the tables severally.”

If that is completely clear to you, then link to Agrippa and study it all. [And pay particular attention to pages 19 through 25 of Part 2 of Book II. Celestial Magic. Some of this is reproduced below for convenience.]

Meanwhile, we might note that in the 5×5, 7×7, and 9×9 magic squares, not only are the diagonal totals the same as the rows and columns, but the two diagonals at equal distances from the center diagonal add to the same total when divided by two. Furthermore, in the right-slanting diagonals, each of the adjacent numbers have a difference of exactly 5, 7, or 9 — depending on the magic square. [However, one may have to complete the cycle to note this. For example, in the 9×9 magic square, going from 78 to 6, involves a 78, 79, 80, 81, 1, 2, 3, 4, 5, 6 sequence — just as ten days from July 25 is August 4.] Adjacent numbers, and numbers with exact differences in sequence seem to be important.

We can look into the numbers associated with these seven magic squares by noting that:

Planet Row Reduced* Inverse Total Reduced* Inverse

(x) (1/x) (y) (1/y)

Saturn 15 6 0.06666666… 45 9 0.022222222…

Jupiter 34 7 0.02941176… 136 1 0.073529412…

Mars 65 2 0.01538462… 325 1 0.003076923…

Sun 111 3 0.00900900… 666 9 0.001501501…

Venus 175 4 0.00571428… 1225 1 0.000816326…

Mercury 260 8 0.00384615… 2080 1 0.000480769…

Moon 369 9 0.00271002… 3321 9 0.000301114…

*As per Numerology.

Other possibilities

notes a Magic Star by Mutsumi Suzuki, i.e.:

Other variations on magic squares include Bimagic Squares (where replacing each number by its square in a magic square results in another magic square) and Border Squares. The latter represents the case where a magic square remains magic when its border is removed. An example is a 3×3 within a 5×5 within a 7×7, and is:

40 1 2 3 42 41 46

38 31 13 14 32 35 12

39 30 26 21 28 21 11

43 33 27 25 23 17 7

6 16 22 29 24 34 44

5 15 37 36 18 19 45

4 49 48 47 8 9 10

Note that in the above example that opposing border numbers always add to 50 (e.g. 38 + 12, 2 + 48, 13 + 37). This sum is the difference between the row totals of the 3×3 (75), and the 5×5 (125), and 7×7 (175).

Variations on magic squares can also be constructed using letters (either in defining the square or as entries in it), such as the alphamagic square and the Templar magic square. An alphamagic is “A magic square for which the number of letters in the word for each number generates another magic square. This definition depends, of course, on the language being used. In English, for example,

5 22 18 4 9 8

28 15 2 becomes 11 7 3

12 8 25 6 5 10

where the magic square on the right corresponds to the number of letters in

five twenty two eighteen

twenty eight fifteen two

twelve eight twenty five

The Templar Magic Square is a magic square-type arrangement of the words in the Latin sentence “Sator Arepo tenet opera rotas” (“the farmer Arepo keeps the world rolling”). This square has been found in excavations of ancient Pompeii.

S A T O R

A R E P O

T E N E T

O P E R A

R O T A S

Another version of this story, and referred to merely as the Sator Rotas magic square comes from , and notes that, “In Rome during the Middle Ages this square was inscribed on a variety of common, everyday objects such as utensils and drinking vessels. It was also found above doorways. It was believed that the square had magical properties, and that making it visible would ward off evil spirits. The words on this square roughly translate to ‘The Creator (or Savior) holds the working of the spheres in his hands.’”

Just read your answer, Eddie, about the number of letters in each number also forming a magic square. So cool! Just what I’d expect from Martin Gardner.

Thanks for that little bit of Culture DAve/Gabby.

Wow! If you add 100 to each number the MAGIC constant of 345 is achieved! 3, 4, 5. Get it?

OK, here’s one. Simplify the following algebraic expression in 26 variables (a thru z):

(x+a)(x-b)(x+c)(x-d)…(x-z).

Zero, as (x-x) is part of the equation

x is usually thev variable.

Actually, DAve is right. The answer is 0. All 26 letters are variables, and nothing in the question said anything special about x.

x^26 +…+ abcdefghijklmnopqrstuvwxjz

Reblogged this on penhaspower and commented:

It actually happens with me… one of the most logical research ever.

Reblogged = copyed = stole

oh I am sorry if you felt bad but I actually admired your research and reblogged only to show my admiration anyways this wont happen again.

These were my comments and opinions not Richards

ok right I didn’t notice that may be because it was my first comment on wordpress and I was too excited to get the reply I thought reblogging here is not a wise decision when u commented anyways do u still think reblogging here is equal to stealing??

What? You’re soliciting an opinion from this interloping fool? (See his other comments further up)

It’s not stealing. As long as you give acknowledgement to the original source then you are fine to do do. My apologies

Eddie. I refer you to the reply given in the case of “Arkell v. Pressdram”

ok thanks for the reply.

Re-blogging is fine as long as you cite the source. Despite what others say. 😛

@Anonymous

> Barry, you went off on a tangent as usual.

Thank you! That is high praise indeed.

To go on a tangent is to swing away from the narrow closed world of the circle. To go infinitely far outside the box – even if it be a circular box or “sphere” as some may call it – and to explore the deeper further reaches of the very universe itself.

It is to be one who does not go round and round in circles thinking the same tiny thoughts over and over again. Instead it is to be one who boldly explores the unreached depths of the perhaps imfathomable world we all form part of.

I am humbled by such praise from one who themselves is so modest as to draw a veil over their own name.

Thank you again @anonymous. You have true insight and the grace to offer praise where you see it. May all your secants be tangents.

@Sheldon Cooper

What a pity that this “magic” is mere number twiddling.

I can see that mathematicians who are clearly jealous of the deeper skills of the magician may have over the centuries developed a deep seated envy.

Yet is is surely simply recognisably an example of professional misconduct to take a word as powerful and resonant as “magic” and use it to mean “adding up trick”.

I am disappointed yet somehow not surprised that mathematicians would stoop as low.

Tommy Cooper. A funny man but a seriously good magician too

Sorry about posting this but there’s not a lot else happening on here. What are the current ages of the following two people? Alan is twice as old as Bob was when Alan was as old as Bob is now.” Sum of their current ages is 49. Similtaneous equations may be required, but I prefer the graphical approach.

There’s a reason why people don’t come here any more! More fool me.

My head is hurting and I’m sorry but I had to do a worked example to understand what was going on, which then led to se’s (and then me kicking myself because I should have been able to do it in my head). Although I’m still having problems drawing it graphically.

Draw a graph: y axis = age, x axis = time. Draw the age timelines of the two men in the xy space and it becomes clear because the lines are parallel and with gradients 45 degrees.

Yeah, I’d got that (and the x+y = 49 line as well) although doing it on a post-it wasn’t the best foundation – it was translating the English into the distance between the parallel lines that was screwing my mind. A good question (rather like “this man’s father…” but to another level)

The first statement reduces to : A = 2(B – (A-B))

or (using the second statement)

49 – B = 4B – 2(49 – B)

49 – B = 6B – 98

7B = 147

B = 21

(using the second statement)

A = 49 – B = 28

I got it sorted by having A and B being the current ages and A-prime and B-prime for being their ages at the key point in the past. 4 unknowns, 4 equations, solved similtaneously, or at least, in order, took me to the answer. It is the magic of English that so few words which in themselves are so plain can lead to such stimulation of the mind, when they refer to the wonder of mathematics. And the fact that you can represent the solution graphically draws out further nuances of the topic.

Sorry, posted from different source then, so didn’t get my name picked up!

This was fun. Had to dissect the language to get it. First, I worked out the obvious unknowns: current ages (A and B), and their former ages (a and b). The “hidden” unknown is their age gap (x).

The givens were that A = 2b when a = B and that A + B = 49.

Of course, x = A – B = a – b; their age gaps being constant. I then saw that x is also B – b, their age gap being equal to the time lapse between a and A and b and B.

I then expressed A and B in terms of x and got that they were 4x and 3x, respectively.

I solved for x using A + B = 49 and got 7.

I got the same results as Gabby for the current ages but not as quickly.

Gabby Bollard, I admire how you quickly translated “Bob’s age when Alan was as old as Bob is now” to “B – (A – B)”. It would appear you immediately saw that their age gap is the same as the time lapsed.

Then again, English is not my first language. 😀

@Edie

A puzzle based on tricky “clever” wording is no puzzle at all. It simply is a word game. These can add nothing to the beauty of the human soul and as such can only be a distraction on our journey of discovery of the depths of human insight and compassion.

I ask you again simply as a favour to your own innate higher self to reflect at least twice before posting any more such frivolities.

You may wish to visit any number of websites devoted to the japanese zen art of the koan. These indeed are puzzles of the highest and most subtle nature often replaying years of gentle reflection and deep study. To truly solve a koan is to go beyond our limited self and to gain a glimpse of out limitless potential.

Please if you should post again in a few years may it be a koan you have truly solved. There then may be great rejoicings here rather than sad pencil scribblings as similtaneous equations are trotted once more out.

Please aspire to your higher self rather than to lower others.

Does your company do a self awareness and interpersonal skills training course?

That you for asking @edie. To humbly ask for assistance is to step onto the path to a solution. Many fail to take even such a first step.

Many courses and many approaches are possible. For best results all should be tailored to the student and at the same time allow the teacher’s strengths to shine forth.

Self-awareness and interpersonal skills are core abilities that I can teach and inspire with. I have many many years of active successful and practical experience in these areas.

You will know that from my contributions both here and elsewhere – such as my own blogs and tweets. The quality of my core work speaks not just for itself but to all who take a bare moment to evaluate it. Even those who initially are somewhat jaded and attempt to belittle my work are won over in time. You yourself may be an example of that.

So thus please ask what you wish and I will endeavor to assist you in all ways that I am capable of.

I would suggest that you have no self awareness or interpersonal skills because you talk over people and annoy intensely. In fact you sound quite aggressive the way you tout your quackery and force your opinions down people’s throats. I would never dream of asking you for assistance or taking your advice on any matter.

Barry Goddard

You are truly one of the most deluded and narcissistic people I have exchanged with on the internet. I know you are full of admiration for your own wisdom, self-awareness and interpersonal skills, but I can honestly say you have a unique ability to stir a negativity in me that I barely recognise. I know you take the unfalsifiable line that those that disagree with you are yet to see or accept your brilliance – and I might agree with you that my own uniquely negative reaction to your posts is my shortfall and not yours – but of course, that too is indistinguishable from narcissism. I am sorry if this comes across as one giant ad hominem, but I honestly think it would be useful for you to know that you come across the very opposite of the kind sage you think you are. I honestly hope this causes you to pause for thought, and allow a little more self-doubt into your life. My apologies if I have misjudged your situation, and there is something else going on that I have been insensitive to.

Nice try, Adzcliff. I think we now know we’re dealing with a psychopath here.

Thanks for this Eddie.

Personally though, I’m not sure he genuinely wishes anyone any ill-will (even if he does appear to look down his nose at his critics). I’m happy to give him the benefit of the doubt that he is just impressively narcissistic, with an impenetrable ego, and absolutely no self-awareness for how he comes across to those who question his self-professed brilliance. He strikes me as the sort of arrogant psychotherapist who would blame the patient for not getting better – or even worse, for their iatrogenia. It’s sort of fascinating in a way, but for some reason it annoys the hell out of me. I almost don’t recognise this reaction in myself? That’s not an emotional response you’d usually associate with a wise, self-aware, interpersonally-skilled teacher. I expect he thinks Socrates, Jesus and Galileo couldn’t please everyone. Anyway, this isn’t good for me…

@adzcliff

Thank you. I accept your apology for your having misjudged and you being insensitive.

It takes courage to admit that one is wrong – especially in such a public forum as an anonymous blog. That you can do so is a rare sign that there may be hope for your future spiritual development. For surely we all contain multitudes of potential once we just throw away the ego clinging that leads us to be judgmental and insensitive to others.

@Edie has decided to go it alone without my inestimable though humbly proffered help. This is of course entirely a personal decision and if it does not work out for the best I will always be there to re-offer my assistance once it can be seen to be needed. In the meanwhile @Edie please continue holding this thought in mind: “What would Barry Do?” It may help comfort you in troubled times.

That one apologies while one other turns their back is a “success” rate that is acceptable to me. I would like to use my skills and insight to help everyone. Yet I am no longer such a wide-eyed optimist to believe that is possible every single day. I will focus on those who request my contributions and look on with kindness on those who do not – even on those who forcibly reject my offers.

Peace and tranquility to us all. Even those who would hide from the world in puzzles and distraction.

A man decides to buy a nice horse. He pays $60 for it, and he is very content with the strong animal. After a year, the value of the horse has increased to $70 and he decides to sell the horse. However, already a few days later he regrets his decision to sell the beautiful horse, and he buys it again. Unfortunately, he has to pay $80 to get it back, so he loses $10. After another year of owning the horse, he finally decides to sell the horse for $90.

Consider the trade-story as if it describes two separate trades, where: In the first trade, the man buys something for $60 and sells it again for $70, so he makes a profit of $10.

In the second trade, the man buys something for $80 and sells it again for $90, so he makes again a profit of $10.

Conclusion: The man makes an overall profit of $10 + $10 = $20.

You can also look at the problem as follows: the total expenses are $60 + $80 = $140 and the total earnings are $70 + $90 = $160. The overall profit is therefore $160 – $140 = $20.

Well done. Where would we be without you (and your alter ego Barry)?

Yes. I am a Wise Man

Fascinating

@Edie

That is a fascinating story. Thank you for telling it.

I knew someone once who owned a sweet shop. They bought bars of chocolate wholesale at one price and sold them individually at another usually higher price. From this they made some money that helped pay the over heads on the building and so on. At the end of the whole process they sometimes made a profit.

Perhaps you could turn that into a grand opera. Singing “We have bought the chocolate. We have sold the chocolate. We have bought the chocolate. We have sold the chocolate” and so on. Repetitious “mantra” like chanting is key to operatic music and to much prayer and to much meditative practice.

Your repetitative story of a horse that was bought and sold and bought and sold falls squarely into that territory. Perhaps that should be set to music and staged and filmed by Steven Spielberg himself.

I am gently kidding you of course as you sometimes try to do with me. But I can see through your gruff exterior to the tiny child who is crying out for help. Perhaps your little pony was sold when you were young and this story of yours is all you have left of it.

May you find your true horse of infinite wisdom and may you not sell it for a minor profit before you have full use of it.

If you know any other stories of retail daring please do tell.

No puzzle today.

Not missing it

No comment.

This is a most unusual paragraph. How quickly can you find out what is so unusual about it? It looks so ordinary that you would think that nothing is wrong with it at all, and, in fact, nothing is. But it is unusual. Why? If you study it and think about it, you may find out, but I am not going to assist you in any way. You must do it without any hints or coaching. No doubt, if you work at it for a bit, it will dawn on you. Who knows? Go to work and try your skill. Good luck!

No letter ‘e’

For someone who wants me to stop posting these ‘off topic’ puzzles, you seem to display an inordinate enthusiasm for solving them.

I impressed myself with how quickly I got this. (I impress easy.) My next question was how long I would have to wait to show off, but then noticed I’ve been beaten to it…

I do not see what is so unusual about a sentence that has no letter E. Many words – perhaps the majority in English – have no letter E.

Your “unusual” sentence has no letter V or J or Z or X. Does that make it five times as unusual or does that made it quite usual indeed.

For those who wish to blight the blog with puzzles they should at least endeavour to get the rest of the blog community on there side by publishing puzzles that have been appropriately peer reviewed and are fair in the ways of solving.

To just publish something random because in your mind it is unusual is the worst form of journalism that leads us towards that perpertrated by the Daily Mail or the Guaridan.

None of us want puzzles when we could be having deeply enriching dialogue that shows us the way to emotional and intellectual liberation. Thus if puzzles are to be foisted on us please make them ones that are wholesome rather than full of holes.

I ask this as a humble representative of the silent majority on this website who have for too long watched the tiny minority enforce their will while pooh-poohing the rest of us for daring to have better and more grounded opinions that do not include a puzzle fixation.

I’ll see what I can do for you, Barry 😉

In case you are confused: please do not confuse me with Gabby Bollard. I am not Ms Bollard. We have it is true similar names. Indeed I suspect Ms Bollard may be a pseudonym chosen to show an infatuation with myself.

Yet we have no connection with each other – other perhaps than subtle psychic resonances of which I will not speak at this time.

Ms Bollard has a certain agenda on this website – as indeed she is free to have and pursue. I have no such agenda other than to humbly assist the truth in any way that I can.

Therefore to consider that Ms Bollard is in some way an “alter ego” of mine is to fall into serious error that will prevent you seeing the true truth of the situation.

The internet is a place in which names can be fluid – and some take advantage of that. Yet still we must offer authentic communication else all is lost. I always strive to be authentic and humble and kind and helpful. These are the qualities by which you may recognise my postings even when others are trying poorly to make fun or play with names or just rightdown confuse us.

Could it be that I was born under the 13th sign, Ophiuchus?

Very few people know their true birth chart “star sign” as the process of assignment is far subtler and more thorough than your Daily Mail astrology columnist would have you believe.

As a long-time practitioner I would say focus less on your star sign and more on your inner potential. You need both of course as one is objective (the cosmos cannot lie) and one is inner subjective (thus easily misread and misunderstood).

Yet until you can safely and accurately read those inner intuitions without bias and filter you will not be able to read the objective truths written in the skies – you will just see additional subjective prejudices and wishful hopes and thinking.

Thus Gabby by all means have your birth chart read – I can offer such a service that is second to none in objective intuition – and use it as a starting point for your inner star trek.

Good to see you’ve given yourself a self-reassuring thumbs-up for you comment, Barry.

Molly has a set of four alphabet blocks. Each side of these blocks is printed with a different letter, making 24 in total. Molly notices that by rearranging the blocks, she can spell each of the following words:

BOXY, BUCK, CHAW, DIGS, EXAM, FLIT, GIRL, JUMP, OGRE, OKAY, PAWN, ZEST

Which letters are on each block?

Easy One

Block 1: A, B, F, J, R, and S.

Block 2: D, E, L, U, W, and Y.

Block 3: C, I, M, N, O, and Z.

Block 4: G, H, K, P, T, and X.

From the word EXAM, we conclude that E and A are not on the same block.

From the word OGRE, we conclude that E and O are not on the same block.

From the word OKAY, we conclude that A and O are not on the same block.

Combining these, we conclude that A, E, and O are on different blocks. Assume that A is on block 1, E is on block 2, and O is on block 3.

From the words BOXY and EXAM, we conclude that X is not on the same block as A (block 1), E (block 2), and O (block 3), so X is on block 4.

From the words BOXY and OKAY, we conclude that Y is not on the same block as A (block 1), O (block 3), and X (block 4), so Y is on block 2.

From the word EXAM, we conclude that M is not on the same block as A (block 1), E (block 2), and X (block 4), so M is on block 3.

From the word OKAY, we conclude that K is not on the same block as A (block 1), Y (block 2), and O (block 3), so K is on block 4.

From the word BOXY, we conclude that B is not on the same block as Y (block 2), O (block 3), and X (block 4), so B is on block 1.

From the words BUCK and JUMP, we conclude that U is not on the same block as B (block 1), M (block 3), and K (block 4), so U is on block 2.

From the words PAWN and JUMP, we conclude that P is not on the same block as A (block 1), U (block 2), and M (block 3), so P is on block 4.

From the word JUMP, we conclude that J is not on the same block as U (block 2), M (block 3), and P (block 4), so J is on block 1.

From the words CHAW and BUCK, we conclude that C is not on the same block as A (block 1), U (block 2), and K (block 4), so C is on block 3.

From the words CHAW and PAWN, we conclude that W is not on the same block as A (block 1), C (block 3), and P (block 4), so W is on block 2.

From the word CHAW, we conclude that H is not on the same block as A (block 1), W (block 2), and C (block 3), so H is on block 4.

From the word PAWN, we conclude that N is not on the same block as A (block 1), W (block 2), and P (block 4), so N is on block 3.

Now, we must still have three letters for block 1, and two letters for each of the blocks 2, 3, and 4. We have the following letters left:

D, F, G, I, L, R, S, T, Z

From the words DIGS, FLIT and GIRL, we conclude that I is not on the same block as D, F, G, L, R, S, and T, so I is on the same block as Z. Furthermore, I and Z are on block 2, 3, or 4.

From the word ZEST, we conclude that Z is not on the same block as E (block 2), so Z is on block 3 or 4.

From the word OGRE, we conclude that G and R are not on the same block as E (block 2), and O (block 3), so G and R are on block 1 or 4, but not on the same block.

From the word GIRL, we conclude that I is not on the same block as G and R (block 1 or 4), so I is on block 2 or 3. Since Z is on block 3 or 4, I and Z must be on block 3. Now we have all six letters of block 3: C, I, M, N, O, and Z.

From the word GIRL, we conclude that L is not on the same block as G and R (block 1 and 4), so L is on block 2.

From the words FLIT and GIRL, we conclude that F, G, L, R, and T are not on the same block as L (block 2), and from the word ZEST, we conclude that S is not on the same block as E (block 2). So D must be on block 2.

Now we have all six letters of block 2: D, E, L, U, W, and Y.

From the words GIRL and DIGS, we conclude that G is not on the same block as R and S.

From the words FLIT and ZEST, we conclude that T is not on the same block as F and S.

Combining this, F, R, and S must be on the same block (block 1), and G and T must be on the same block (block 4).

Now we have all six letters of all blocks:

Block 1: A, B, F, J, R, and S.

Block 2: D, E, L, U, W, and Y.

Block 3: C, I, M, N, O, and Z.

Block 4: G, H, K, P, T, and X.