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Programming Enigma Puzzles

28 March 2016

Posted by on **From New Scientist #2330, 16th February 2002** [link]

An example of a letter sum is:

ABC + DCEF = AEFB.

That is to say word + word = word, where each word is a string of letters of any length. An example of an

for the above sum is:answer537 + 4726 = 5263.

We are concerned with letter sums that have exactly one answer. For each such letter sum we produce its A-number by taking its answer and discarding the + and =. For example if the above letter sum had only the answer given above then its A-number would be:

53747265263.

What are the four smallest A-numbers we can get by this process?

[enigma1174]

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This Python program uses the

SubstitutedSum()solver from theenigma.pylibrary. It runs in 4.5s.Solution:The first four A-numbers are 1910, 9110, 89998, 98998.The corresponding single solution sums are:

These are the only A-numbers less than 6 digits.