We don’t post many of these because they take sooooo long to think and develop, but here is our new Quirkology video – The Incredible Candles! Hope that you enjoy it.

“People speak sometimes about the “bestial” cruelty of man, but that is terribly unjust and offensive to beasts, no animal could ever be so cruel as a man, so artfully, so artistically cruel.”
― Fyodor Dostoyevsky

A magician can perform magic yet a trickster can only show tricks.

Clever though this trick is it could never work in the real world. It is forever limited to the two dimensional surface that is a movie with a camera that must be at a precise angle and all the lighting just so.

True magic will work anywhere and we are all capable of it if only we cease to listen to the voices that tell us it is impossible. Those voices truely themselves do not exist being just imaginary worries we conjure from nowhere.

The ‘Pepper’s Ghost’ illusion has been performed on stage many times, so is not just limited to 2D.
And “A magician can perform magic”? What magician is that, then – Harry Potter?

As any humble historian of stage magic will know without question “pepper’s ghost” was invented by Henry Dircks who sold the design of the trickery to John Henry Pepper in 1862.

Yet it is indeed a 2 dimension effect. The ghost characters may appear to be fully formed and moving on the stage with the real actors. They are not. They are in the same position as the “ninja” in the candle trick video. Worse still they are often strapped onto trundles and hauled back and forth by ropes while under the stage approx in the position of the orchestra pit. They have little freedom to move freely.

It is carefully constructed trickery based on calculated lines of sight and a large sheet of glass. Prof Wisemans modern version of the trick is in miniture what Dircks designed and Pepper staged in the 1860s decade and later.

Yet true three dimensional magic is all around us. Look at the stars. Look back at our hearts. Reach into your mind and find that grain of sand that contains the entire universe. All is not just connected it is also interconnected to everything else.

Thus a true magician is simply a realist who sees what is before him and then sees deeper into it than the more hidebound “rational” surface thinkers.

Thus a true magician can see out hearts in the stars and our lives in the sky. This is simple every day magic that transcends trickery and exposes us to the depths of reality that we already encompass.

It can be good to be fooled by a simple trick. Yet we must allow ourselves to be encouraged to greatness by true magic.

I could not rest easy if I thought there were others who fail to see this simple fact of the cosmos.

Using the operations of addition, subtraction, multiplication, division (as many or as few of each as you need) and using the four digits 3, 3, 8 and 8 each once and only once, make an expression equalling 24.

In the traditional spirit of RW’s usual request for his now seemingly abandoned “Friday Puzzles” I will not give my answer until after the weekend. I know that some regular posters would break that “embargo” and give answers before the requested time. That was always a little disrespectful and was disturbing to us who wishes to discuss the Puzzle without giving away it’s secrets.

Yer be that as it may be. I can see an even better answer than the “official” one that I think you think we would be groping towards.

As in the Real World to solve a problem with resources to spare is a most welcome art. No one except perhaps Local Government ever is happy with spending their entire budget to implement a course of action. There should always be savings and reserves if you have striven for the most effective and efficient solutions.

In that spirit I offer two ways to get to 24 using only HALF the numbers you have given as starting seeds. Those ways are 3 x 8. And 8 x 3.

They would be correct and indeed optimal answers each scoring 10 points on Countdown which is where this type of puzzles is most often seen on our television screens.

I hope that my humble yet ingenious offerings spur similarly like minded posters to even higher feats of efficiency.

I am sorry to hear you were unable to solve the Puzzle @ChrisR set.

Yet you could at least have tried and posted your workings so we who can solve Puzzles could more accurately assess where your areas of weakness are. That would enable us better to mentor you in future. Thus we all would learn something.

I did not write that I had developed two Solutions. I fear if you misread my response then you may perhaps have also misread the original Puzzle. That alone may account for you’re being unable to offer a solution. Careful attention to deal is a necessary step when dealing with Puzzles where the wording is oftsoever crucial to the handling of subtle nuances.

Yet still I have allowed your comment to become prophetic as I have cogitated momentarily on the Puzzle and thus another Solution was immediately obvious to me.

These are just two ways:

24 = 3! x (8/8 + 3)

24 = (8 / (8 – 3 – 3))!

Thank you once again for your support and comments.

The subtle twist to the wording was that you can use as much multiplication as you need. And the exponentiation operation (!) is simply a shorthand for much multiplication.

Thank you for your questions. I may help you to gain understanding if you carefully read my answers.

Use of round brackets is a typographical convention because smaller fonts and underlining is not possible on this blog. Thus if I want to set the equation ONE OVER (TWO PLUS 1) I would be forced to use round brackets rather than upper and lower numbers with a line between them.

(If you wish to be pickily pedantic the line between them would also be disallowed by ChrisRs original rules. Yet here we must be pragmatic and read between the lines (pun intended) and know that he would allow that).

As for the ! – the original Puzzle allows for that as previously stated. It is simply a shorthand for as much multiplication as is needed. The original Puzzle allows the use of multiplication. Yet it does not restrict the symbols that can be used to represent it.

I could of course have written the Solutions using Reverse Pollish which would have no round parenthesis at all. Yet I fear that the less mathematically sophisticated readers of the blog would struggle to understand that notion that is so natural to those of use who immerse ourselves in star chart calculations each day.

I trust that I have fully answered your questions and opened indeed your mind to some of the subtler issues surrounding an apparently trivial Puzzle.

Hmm, well if it can only be solved using the factorial function, then I don’t think Chris R worded it very well, as he limited it to the four arithmetic operations. The argument “factorial is just a shorthand for multiplication” doesn’t wash with me, as eg 4! is 4 x 3 x 2 x 1 but 2 wasn’t available in the stated question; I could just as much argue that the function MEAN(a,b) = (a+b)/2 is acceptable because it only involves addition and division, and then give the answer MEAN(3×8, 3×8).

Chris – can you tell us what solution you had in mind?

Now that’s an answer I can accept. (I think brackets are allowed because they just show the order in which the operations are performed). Nice one, Eddie.

It is odd indeed that you will “accept” an answer that has parenthesises in it when your earlier questioned their very use. It may be that you are unconsciously deciding only to accept certain answers because they come from certain people. Freud and his ilk would be very interested in your process of selection.

Similarly you do not allow the 2 in 4! yet you are happy with the 2 in 8/3. This is mayve perhaps special pleading to exclude certain responders for emotional reason related to your own psyche rather than rational thought process.

I am not dismayed by what some would portray as a form of cyber bullying via the invention of reasons to exclude and this dehumanise those you choose to treat as unsuitable to provide answers.

Instead I am fascinated by this dance of human depths exposed by your responses.

I wish that you will think deeply on these issues and arise with a deeper understanding of your own thought and feeling processes as a resultant outcome.

Your enhanced insight from that exercise will benefit yourself and all around you immensely.

I never questioned the use of parentheses – that was someone called Geography Kilometres, who is nothing to do with me, despite obviously paying tribute to my nickname with his!

Barry, if you add up all the numbers in 4! you get 4+3+2+1=10. If you add up all the numbers in 8/3 you get 11, which is more than 10. So this must be right.

Sitting with a Rubik’s cube on my desk (that’s the cube on my desk, not me) I was able to understand what this looks like and therefore where the other ends of the diagonals are. And hence, to come up with an answer.

“People speak sometimes about the “bestial” cruelty of man, but that is terribly unjust and offensive to beasts, no animal could ever be so cruel as a man, so artfully, so artistically cruel.”

― Fyodor Dostoyevsky

A magician can perform magic yet a trickster can only show tricks.

Clever though this trick is it could never work in the real world. It is forever limited to the two dimensional surface that is a movie with a camera that must be at a precise angle and all the lighting just so.

True magic will work anywhere and we are all capable of it if only we cease to listen to the voices that tell us it is impossible. Those voices truely themselves do not exist being just imaginary worries we conjure from nowhere.

Very clever…..but the reflection of the plastic glass was evident at 00:14 when I watched (not that I was able to figure out the trick though)

This video needs more Quirkoolgy Goat.

The ‘Pepper’s Ghost’ illusion has been performed on stage many times, so is not just limited to 2D.

And “A magician can perform magic”? What magician is that, then – Harry Potter?

Don’t question Barry or he’ll go off on one.

What do we all think of the Edzard Ernst/Prince Charles complementary medicine story? A travesty I call

it.

@Jill Burton

Thank you for your support and comments.

As any humble historian of stage magic will know without question “pepper’s ghost” was invented by Henry Dircks who sold the design of the trickery to John Henry Pepper in 1862.

Yet it is indeed a 2 dimension effect. The ghost characters may appear to be fully formed and moving on the stage with the real actors. They are not. They are in the same position as the “ninja” in the candle trick video. Worse still they are often strapped onto trundles and hauled back and forth by ropes while under the stage approx in the position of the orchestra pit. They have little freedom to move freely.

It is carefully constructed trickery based on calculated lines of sight and a large sheet of glass. Prof Wisemans modern version of the trick is in miniture what Dircks designed and Pepper staged in the 1860s decade and later.

Yet true three dimensional magic is all around us. Look at the stars. Look back at our hearts. Reach into your mind and find that grain of sand that contains the entire universe. All is not just connected it is also interconnected to everything else.

Thus a true magician is simply a realist who sees what is before him and then sees deeper into it than the more hidebound “rational” surface thinkers.

Thus a true magician can see out hearts in the stars and our lives in the sky. This is simple every day magic that transcends trickery and exposes us to the depths of reality that we already encompass.

It can be good to be fooled by a simple trick. Yet we must allow ourselves to be encouraged to greatness by true magic.

I could not rest easy if I thought there were others who fail to see this simple fact of the cosmos.

It’s Friday – try this

Using the operations of addition, subtraction, multiplication, division (as many or as few of each as you need) and using the four digits 3, 3, 8 and 8 each once and only once, make an expression equalling 24.

@ChrisR

In the traditional spirit of RW’s usual request for his now seemingly abandoned “Friday Puzzles” I will not give my answer until after the weekend. I know that some regular posters would break that “embargo” and give answers before the requested time. That was always a little disrespectful and was disturbing to us who wishes to discuss the Puzzle without giving away it’s secrets.

Yer be that as it may be. I can see an even better answer than the “official” one that I think you think we would be groping towards.

As in the Real World to solve a problem with resources to spare is a most welcome art. No one except perhaps Local Government ever is happy with spending their entire budget to implement a course of action. There should always be savings and reserves if you have striven for the most effective and efficient solutions.

In that spirit I offer two ways to get to 24 using only HALF the numbers you have given as starting seeds. Those ways are 3 x 8. And 8 x 3.

They would be correct and indeed optimal answers each scoring 10 points on Countdown which is where this type of puzzles is most often seen on our television screens.

I hope that my humble yet ingenious offerings spur similarly like minded posters to even higher feats of efficiency.

Well if Barry if genuine, he can return here on Monday morning and post the TWO solutions he has found. I’m looking forward to it.

@MathMiles

I am sorry to hear you were unable to solve the Puzzle @ChrisR set.

Yet you could at least have tried and posted your workings so we who can solve Puzzles could more accurately assess where your areas of weakness are. That would enable us better to mentor you in future. Thus we all would learn something.

I did not write that I had developed two Solutions. I fear if you misread my response then you may perhaps have also misread the original Puzzle. That alone may account for you’re being unable to offer a solution. Careful attention to deal is a necessary step when dealing with Puzzles where the wording is oftsoever crucial to the handling of subtle nuances.

Yet still I have allowed your comment to become prophetic as I have cogitated momentarily on the Puzzle and thus another Solution was immediately obvious to me.

These are just two ways:

24 = 3! x (8/8 + 3)

24 = (8 / (8 – 3 – 3))!

Thank you once again for your support and comments.

The subtle twist to the wording was that you can use as much multiplication as you need. And the exponentiation operation (!) is simply a shorthand for much multiplication.

Fascinating as ever Barry but where in the question does it say one may use parentheses or the factorial sign?

@Geography Kilometres

Thank you for your questions. I may help you to gain understanding if you carefully read my answers.

Use of round brackets is a typographical convention because smaller fonts and underlining is not possible on this blog. Thus if I want to set the equation ONE OVER (TWO PLUS 1) I would be forced to use round brackets rather than upper and lower numbers with a line between them.

(If you wish to be pickily pedantic the line between them would also be disallowed by ChrisRs original rules. Yet here we must be pragmatic and read between the lines (pun intended) and know that he would allow that).

As for the ! – the original Puzzle allows for that as previously stated. It is simply a shorthand for as much multiplication as is needed. The original Puzzle allows the use of multiplication. Yet it does not restrict the symbols that can be used to represent it.

I could of course have written the Solutions using Reverse Pollish which would have no round parenthesis at all. Yet I fear that the less mathematically sophisticated readers of the blog would struggle to understand that notion that is so natural to those of use who immerse ourselves in star chart calculations each day.

I trust that I have fully answered your questions and opened indeed your mind to some of the subtler issues surrounding an apparently trivial Puzzle.

Brackets and factorials are usually allowed in this type of question. Can you do it without them?

What’s more annoying is the plethora of solutions which I didn’t see.

Eddie,

To help me in future are there any other items that are “usually allowed in this type of question”? It would be helpful to know.

No. I couldn’t answer the question as stated, but I could arrive at 24 using factorials as well.

Hmm, well if it can only be solved using the factorial function, then I don’t think Chris R worded it very well, as he limited it to the four arithmetic operations. The argument “factorial is just a shorthand for multiplication” doesn’t wash with me, as eg 4! is 4 x 3 x 2 x 1 but 2 wasn’t available in the stated question; I could just as much argue that the function MEAN(a,b) = (a+b)/2 is acceptable because it only involves addition and division, and then give the answer MEAN(3×8, 3×8).

Chris – can you tell us what solution you had in mind?

8/(3-(8/3))

Now that’s an answer I can accept. (I think brackets are allowed because they just show the order in which the operations are performed). Nice one, Eddie.

That was it (!)

@MathMiles

It is odd indeed that you will “accept” an answer that has parenthesises in it when your earlier questioned their very use. It may be that you are unconsciously deciding only to accept certain answers because they come from certain people. Freud and his ilk would be very interested in your process of selection.

Similarly you do not allow the 2 in 4! yet you are happy with the 2 in 8/3. This is mayve perhaps special pleading to exclude certain responders for emotional reason related to your own psyche rather than rational thought process.

I am not dismayed by what some would portray as a form of cyber bullying via the invention of reasons to exclude and this dehumanise those you choose to treat as unsuitable to provide answers.

Instead I am fascinated by this dance of human depths exposed by your responses.

I wish that you will think deeply on these issues and arise with a deeper understanding of your own thought and feeling processes as a resultant outcome.

Your enhanced insight from that exercise will benefit yourself and all around you immensely.

I never questioned the use of parentheses – that was someone called Geography Kilometres, who is nothing to do with me, despite obviously paying tribute to my nickname with his!

@MathMiles

Thank you for your apology.

Well, Barry, I accept your gracious admission that you were wrong.

Barry, if you add up all the numbers in 4! you get 4+3+2+1=10. If you add up all the numbers in 8/3 you get 11, which is more than 10. So this must be right.

I think the trick will be far more impressive if you did it with four candles

fork handles?

You’re a sharp one

What is the angle between two diagonals meeting at a vertex on adjacent faces of a cube?

Sitting with a Rubik’s cube on my desk (that’s the cube on my desk, not me) I was able to understand what this looks like and therefore where the other ends of the diagonals are. And hence, to come up with an answer.

You clever old stick, but you may need to check with Eddie that Rubik’s Cubes are “usually allowed in this type of question.”

Yes. Rubik’s cubes are allowed. Hungarian invention, you know.

Off the top of my head, 54.7 degrees

Sorry – meant to reply under here. My answer is posted below.

I’ve worked out the answer using the same idea as Chris by the sound of it. DAve’s answer is close but a little too low.

54.71 degrees?

A bit higher… (well, if you are going up in steps of 0.01, quite a lot higher…)

DAve, don’t be so obtuse!!

a year ago today