**From New Scientist #2537, 4th February 2006**

Regular enigmatists will have encountered many puzzles by Susan Denham but many may not know that this name is a pseudonym, Sue Denham and pseudonym being approximate homophones. So it is appropriate that I can set you the following sum, in which digits have been consistently replaced by letters, different letters representing different digits.

But there is no solution to it in base 10. You must tackle the puzzle in the base that allows just one possible value for PSEUD. Your task is to find that value of PSEUD, convert it into its equivalent in base 10 and find the base 10 equivalent of PSEUD as your answer.

According to this article in the Independent, Susan Denham is a pseudonym of Dr Victor Bryant.

[enigma1377]

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My original Python program ran in 2.1s (under PyPy), but using the [[

`SubstitutedSum()`

]] solver from theenigma.pymodule I can get a much neater program that runs in only 335ms.Solution:PSEUD is 156454 (in decimal).The sum is in base 11, and

PSEUD= A7601 (base 11).