# Sunday Times Teaser 2826 – By Heck!

*by Stephen Hogg*

#### Published: 20 November 2016 (link)

The registration number of my old car consists of three consecutive letters of the alphabet in reverse order, followed by a three-figure number consisting of the same digit written three times, followed finally by a single letter.

I am a fan of “hex” (i.e. arithmetic in base 16, with “digits” 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F) and I realised that the registration number looked like a number in hex. So I worked out its equivalent value in our usual base-10 arithmetic. Miraculously the answer was a nine-figure number that used all nine of the non-zero digits.

What is the registration number?

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This week there don’t seem to be any issues with the puzzle text.

There are 4×10×6 = 240 possibilities for the registration number which can be examined by a straightforward program to find those which correspond to an appropriate decimal number.

This Python program runs in 50ms.

The requirement that the decimal representation does not contain the digit zero is superfluous.

The

enigma.pylibrary is available at [ http://www.magwag.plus.com/jim/enigma.html ].