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.

1. z says:

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

1. ChrisR says:

yes, 1 multiplied by 3 = 1

2. ChrisR says:

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.

3. Mike Ryan says:

Yes ten minutes

2. cburubjf says:

is it :O

3. Anne Elk says:

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

1. Steve says:

I concur.

4. Dong says:

anyone learnt to divide by 7?

1. Richard says:

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

2. Phil says:

>>anyone learnt to divide by 7?

That’s the way I did it..

5. Mark C says:

Easy…

6. Mark C says:

@Dong – apparently not…

7. ChrisR says:

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

1. ChrisR says:

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

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

1. Steve says:

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

2. @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.

3. digitaljoel says:

Same here. Yay for math.

9. Matt says:

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.

1. ChrisR says:

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

2. Paul says:

Snap!

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

4. Anonymous says:

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

5. Lazy T says:

10 mins of scribbling ‘hangman style’ and I got it.
Miranda’s tip for the Numberphile video made it all clear, thanks.

6. Lazy T says:

oops sorry, all messed up, wrong vid too

10. Martijn h says:

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

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

1. Megan T says:

No, it isn’t…

2. Greg says:

Not in my answer it isn’t.

3. kroketje says:

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

12. Navneeth says:

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.

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

14. 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.

15. Pitmonster says:

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

16. Eddie says:

This puzzle is exceltly what it was invented for.

17. Slange Navarr says:

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

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

2. Slange Navarr says:

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

3. Eddie says:

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

4. Slange Navarr says:

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

5. Phil McCavity says:

I am Spartacus

6. Slange Navarr says:

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

About as funny as that cancer Janus.

7. Slange Navarr says:

Disregard that. I apologise for my own stupidity.

8. DeepField says:

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…

9. Slange Navarr says:

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.

18. Alma says:

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. . .) 🙂

1. 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.

19. ME says:

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. 🙂

20. 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 🙂

21. Tony H says:

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…

1. 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.

2. 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.

22. kroketje says:

pffff…. it took about 6-7 minutes.

23. jh says:

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!

1. jh says:

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.

2. I Luv Spoilers says:

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

3. 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.

4. jh says:

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.

5. Slange Navarr says:

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

25. 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.

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

27. mittfh says:

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

28. Kristian says:

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

29. Mick says:

with some logic approach still 20 min.

30. 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.

1. jh says:

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

2. Ben says:

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.

31. rmb says:

5 minutes (using pen and paper)

32. Stevie says:

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.

33. Duncan says:

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.

35. @Sceptic_Tank says:

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!

36. 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!)

1. Duncan says:

Wow, that’s cool!

2. I Luv Spoilers says:

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

37. Phil H says:

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.

38. 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.

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

40. 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.

41. Anonymous says:

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

42. Paul Durrant says:

1. Dougal McTavish says:

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

2. Dougal McTavish says:

My mistake. I should have read the question more carefully

43. SkinnyInny says:

44. John says:

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

45. Anonymous says:

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

46. du Lisoy says:

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

47. b says: