**From New Scientist #2874, 21st July 2012** [link]

I was teaching my nephew about arithmetic progressions – sequences like 17, 23, 29,… 677,… in which the common difference between successive terms is a constant. In this one the difference is 6 and the 111th term is 677. Later, he devised his own progression, but consistently replaced digits with capital letters, with different letters for different digits. His sequence was ONE, TWO,… THREE,… with the 111th term being THREE. The common difference was odd and more than the number represented by SIX.

Tell me the number represented by SENT?

[enigma1707]

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The following Python program runs in 160ms.

Solution:SENT = 4236.My solution gives a unique answer, I think:

– after code

The

breakstatement makes it stop after it finds the first solution. If you remove that it should find the other possible value forSIX.