Please do **NOT** post your answer, but do say if you think you have solved the puzzle and how long it took. Solution on Monday.

I am thinking of a 5-digit number. If you put ‘1’ at the beginning of the number you get a number that is three times smaller than if you put ‘1’ at the end of the number. What number am I thinking of?

I have produced an ebook containing 101 of the previous Friday Puzzles! It is called **PUZZLED** and is available for the **Kindle **(UK here and USA here) and on the **iBookstore** (UK here in the USA here). You can try 101 of the puzzles for free here.

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So if you put a one at the beginning to make a six digit number?

yes, 1 multiplied by 3 = 1

well, that comment didn’t come out as I typed it…don’t use angle brackets…

1-followed by 5 digit number answer (making 6 digits), multiplied by 3 = 6-digit number made up of 5-digit answer followed by a 1.

Yes ten minutes

is it :O

Tried for a couple of minutes. Recognised my own limits! No chance.

I concur.

anyone learnt to divide by 7?

I did using a calculator 🙂 my 7 times table is a bit rusty when I get beyond 28 or so

>>anyone learnt to divide by 7?

That’s the way I did it..

Easy…

@Dong – apparently not…

I’ve got an / the answer in about 4 minutes but had to resort to Excel. I could work out the last digit and guess the first OK which helped but mind went blank on how to do the rest – although I’ve just thought about it a bit more and may have a paper and pen approach over lunchtime

Couldn’t wait until lunch – and did it in about 2 minutes (and knowing the answer beforehand didn’t really help); should have persevered

Solved. It took me 2 minutes using a simple algebraic rearrangement.

I rather suspect not. Algebra doesn’t do string manipulation.

@steve Adding one hundred thousand is not a string manipulation, and neither is multiplying by ten and adding one.

see the comments below where the algebraic equation is posted. There are also tips on on solving for X further down it too.

Same here. Yay for math.

Nice puzzle. 2 minutes with pen and paper – without giving too much away, when I saw the answer I recognized the sequence of digits which might have led to a short-cut.

oh yes, nice – discussion (on Monday) as to why that is

Snap!

Oh, yeah! Of course. I remember the Cyclic Numbers video Numberphile did last month.

7 mins of scribbling ‘hangman style’ and I got it, then watched Miranda’s vid and all became clear.

10 mins of scribbling ‘hangman style’ and I got it.

Miranda’s tip for the Numberphile video made it all clear, thanks.

oops sorry, all messed up, wrong vid too

Less than 2 min. Straight forward, but needed pen and paper to calculate.

Took 5mins – pen and paper approach… as Dong hinted, the answer is a multiple of 7…

No, it isn’t…

Not in my answer it isn’t.

No, my answer is also “not” a multiple of 7

@dong yes, I came down to 7x = ?????

About a couple of minutes working it out with pen and paper.

To the rest of the solvers: there is a solution when you append a ‘1’ at either end and make it six-digit numbers.

Solved! Admittedly, I changed the wording of the puzzle to “make a cup of tea”. Once I did that though, the answer was simple.

Got it by pen and paper in about four minutes. I recognized the pattern after Dong pointed it out, but didn’t see it in time for it to help with the solution.

Did it in under 2 minutes, although I did use Excel

This puzzle is exceltly what it was invented for.

We can make an equation:

3(100000 + x) = 10x+1

Adding 100000 puts a 1 at the front of a five-digit number, and multiplying by 10 and adding 1 puts a 1 at the end of a number

This how I approached this problem, but I deemed that equation to be ‘posting the answer’ 😛

You are not Slange Navarr. I am. Please do not use other people’s names; it gets confusing.

Can’t believe it was that simple. I didn’t do it that way. Damn!

No, I am Slannge Navarr. Both of you are frauds

I am Spartacus

Brilliant. Do you often have problems with the spelling of your own first name in that case?

About as funny as that cancer Janus.

Disregard that. I apologise for my own stupidity.

I sometimes suspect that the real reason Dr. Wiseman posts these puzzles is to study the people who cannot help but post the answers. Almost every time there is somebody…

Stunningly hilarious as ever, Janus. You must give yourself a nosebleed, you old flap, you’re so sharp… Now see if you can manage a few full stops and a sentence with more than a handful of simple words. Humour’s loss would be grammar’s gain, and you might even be able to convince your carers that you are somebody else.

Oh no – more numbers stuff. 😦 Please let’s have more logic, word and “story” brainteasers, for those of us who enjoy these things but are not mathematically-minded? (Are there are any more people out there like me, who just go “eh??” at most of the numbers puzzles. . .) 🙂

I much prefer the numbers stuff, mostly because I can almost always get those and that leaves me feeling like quite a genius, as opposed to the logic puzzles which generally leave me feeling like a fool.

took a minute to work this out. I used the same equation that someone posted earlier.

Interestingly if abcde is a solution then so is abcdeabcde (albeit with 10 rather than 5 digits). I.e if 12345 were a solution (which is is not) then 1234512345 would be too.

This is also true for all multiple repetitions of the digits, I have a remarkable proof of this but this comment box it too small to contain it. 🙂

Did it, took about 5 minutes, easy once I expressed it the right way. I started badly though working through the numbers (I figured the first couple of digits but it started getting difficult) so much easier using algebra 🙂

Don’t be confused by the divide by 7 thing people – neither number is a multiple of 7. One of them is an interesting multiplier of 7 however, and that’s the point…

If you use the algebraic equation given above, you’ll rearrange to 10X-3X = (?x?00000)-? then simplify to x= ((?x?00000)-?)/7 so there is a divide by 7 in the solution.

Edit: should have used * not x for multiply..

If you use the algebraic equation given above, you’ll rearrange to 10X-3X = (?*?00000)-? then simplify to x= ((?*?00000)-?)/7 so there is a divide by 7 in the solution.

pffff…. it took about 6-7 minutes.

I consider myself a “mental calculation” challenged person, even so with a pen a paper I got it in about 5 minutes.

Very nice puzzle!

For those who think the puzzle was spoiled when they saw the equation, you can try to find another method, and you don’t need Excel either.

Mike@parax’s post only served to enhance my enjoyment jh.

Why don’t you post your other Excel free method now – or on Monday if you are a dyed in the wool spoilerphobe?

One minute by the way

I tried not to give too much away, you still need to understand what the ??? are and why in my tips above and I only posted those after the full equation was posted.

It was the first one to claim that was Slange Navarr (?) who really spoilt the puzzle. And no, I won’t post the algebra-Excel-free method, at least not before Monday. I belive it’s the method a lot of people has used.

Exactly, jh. But it wasn’t me. It was that Hugh Janus cancer using my anagram name (for reasons known only to himself and presumably the poor sod who pours his drinks). The wee man thinks it’s amusing to spoil puzzles using someone else’s name. I almost feel sorry for the pathetic bowl of pus.

Spent ages trying to do it by trial and error, got within 3 of the correct answer, then realised it could be done easily with an equation.

Time: Far too long

I’m not mathematician and this seemed too easy… waiting for Monday to see whether my comprehension of the question was correct in the first place.

Took me a few minutes, then kicked myself when I saw the answer.

Nice little algebra problem – although it’s been a while since I last worked with numbers as large as 300,000…

Pretty cool puzzle. Spent a few minutes randomly attacking it before I realised a proper way to solve it. 5 minutes all in all.

with some logic approach still 20 min.

Is the 1 that we’re putting at the start and finish part of the five digits, or is it a sixth digit? I assume the latter but want to be sure.

The puzzle asks for a 5 digit number, let’s say abcde. If we “add” a 1 digit to the left, the result is 3 times smaller than putiing the 1 digit at the right, so:

1abcde is 3 times smaller than abcde1

We’re asked to “put ’1′ at the beginning of the number” (not add), which could mean 1bcde, rather than 1abcde – though I assume the latter is what’s meant.

5 minutes (using pen and paper)

Unlike the constipated mathematician, I couldn’t work it out with a pencil! The grey cells certainly weren’t coming to my assistance on their own and I didn’t know what to do on excel to determine an answer.

I quit and await the answer on Monday with great interest.

If you can do algebra this is straightforward. I hope we get something a bit different next week.

6 min. Using pen an paper and algebra.

Totally flummoxed. And I enjoy Deepfield’s comment. That never occurred to me – so Machiavellian! We are all guinea pigs!

PS I got as far as divisor is 7, but, according to my predecessors that’s wrong.

I had been frustrated at the simplicity of most recent challenges so well done Prof – you well and truly stuffed me on this one. Please make sure that you explain how the solution is derived on Monday. Ta!

Nice puzzle. About 3 or 4 minutes. Brute force. Then algebra.

This also has a solution:

I am thinking of a 5-digit number. If you put ’2′ at the beginning of the number you get a number that is three times smaller than if you put ’2′ at the end of the number. What number am I thinking of?

(It’s a different answer! to the first problem, though has an interesting relationship!)

Wow, that’s cool!

85714….now that does have an interesting rationship with whatever the answer is…..

Nice puzzle, although I misread the question and got the 3 times bit round the wrong way at first. Time to have a lay down after using my brain for 1.5 minutes.

Simple equation, about a minute or so. Only as long as it took to write it down and work it out.

At first I thought it was going to be simultaneous equations or a quadratic equation, but it was even easier than that.

About 1 minute to work out the formula on paper, plus the time to start up “calc” to do the final calculation.

Another of these ‘fuck you’ puzzles…I do not attempt them any more. To successfully complete them they require knowledge of and facility in algebra and tuition in the ‘number’ strand of mathematics…areas in which my primary and secondary teachers were woefully deficient in their learning attempts with me.. rather, they were insolent bullies who degraded learners such as myself.

Masala – a puzzle creator working for The Guardian newspaper – also creates them.

That was easy it’s my pincode for online banking.

Nice puzzle, with a unique answer. About ten minutes.

It doesn’t have a unique answer – it has many

My mistake. I should have read the question more carefully

Got this in under 25 seconds. Admittedly I used Google.

Managed it in about 5 min using trial method working from leftmost digits. Used Wolfram app to speed multiplication.

“3 times smaller”, logically is a nonsensical statement!

< 2 minutes 🙂

I would suggest there are 2 solutions. Algebra is the better way.

about 1 minute. used algebra

Totally failed. AND I did Pure and Applied Maths at A Level. What does that prove?

Anyway, now I see it, the ‘trick’ is to use (10*x)+1

My algebra was …… well, completely wrong, but it seemed logical at the time until it resolved into nonsense. I hate being wrong but love learning new ‘tricks’, or being brought up short by brighter minds. Nothing wrong with that.

10 minutes in… and i’m quite puzzled.