# Sunday Times Teaser 2772 – Madam I’m Adam

*by Victor Bryant*

#### Published: 8 November 2015 (link)

Adam noticed that today’s Teaser number was a four-figure palindrome. He told me that he had written down another four-figure palindrome and he asked me to guess what it was. I asked for some clues regarding its prime factors and so he told me, in turn, whether his number was divisible by 2, 3, 5, 7, 11, 13, … Only after he had told me whether it was divisible by 13 was it possible to work out his number.

What was his number?

As written above this teaser is unsolvable – the first two sentences should read: “My friend chose a four digit palindrome and asked me to guess it.”

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I used a few useful routines from the

enigma.pylibrary [ http://www.magwag.plus.com/jim/enigma.html ].Here’s a slightly different version of the program that shows which palindromes have shortest unique answers as each prime is reached.

So to solve the stated problem it stops at N=13, but by specifying different N on the command line we can see when the other palindromes become distinguishable.