# Sunday Times Teaser 2624 – Is It 2013?

*by Victor Bryant*

#### Published January 6 2013 (link)

I have in mind a four-figure number. Here are three clues about it:

Like 2013, it uses four consecutive digits in some order.

It is not divisible by any number from 2 to 11.

If I were to tell you the ________ digit, then you could work out my number.

Those clues would have enabled you to work out my number but unfortunately the printer has left a gap: it should have been the word “units” or “tens” or “hundreds” or “thousands”.

What is my number?

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Here is my version:

Here is an alternative version (the latter part of this is similar to that in Arthur’s version below):

Another version (with some input from Brian):

Hi Brian,

How could we deduce the number from the output of this program if we knew the digit in a particular position?

Hi Naim,

If we list the numbers according to their top digit we have:

1423,

2143, 2341, 2413, 2543

4231, 4253, 4321, 4523, 4567, 4657

5647, 5867, 6547, 6857,

8567

So if we knew that the top digit is 1 we would then know the number is 1423. Similarly, if the top digit is known to be 8 we would then know that the number is 8567.

But since, in this case, there are two answers, we can’t tell which is correct unless we know the top digit.

But if we now list the numbers with the same second digit, maybe there will be only one answer so we don;t need to know the digit. And we can build lists for the third and the fourth digits as well.

And, hopefully, one of these lists will have only one possible answer.

Dear Brian,

For your explanations, 2013 times “Thank you”

and I wish a happy new year to you.

Using the amended version of the question:

It is possible to solve many of these ST problems without a computer program. I help students prepare for numerical aptitiude tests, no computer needed, just a mix of O & A level maths.

Hi David,

You are right but this site is about computer solutions using Python. The site at https://sites.google.com/site/sundaytimesteasers/ is one where non-computer solutions are discussed.