**From New Scientist #2262, 28th October 2000** [link]

Harry, Tom and I each found a set consisting of a 4-digit perfect square, a 3-digit perfect square and a 2-digit perfect square that between them used nine different digits; but none of us could add a 1-digit square with the unused digit because 9, 4, 1 and 0 all appeared in each of our three sets. No two of us found exactly the same set; none of the squares in my set appeared in either Harry’s set or Tom’s set. There is one further set that none of us found whose unused digit is again not itself a perfect square.

List in ascending order the three squares in this set that none of us found.

[enigma1106]

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This Python program uses the

SubstitutedExpression()solver from theenigma.pylibrary to solve the embedded problem and find possible sets that satisfy the conditions Tom, Dick and Harry are looking for, and then examines which arrangement of possible solutions satisfies the remaining conditions. It runs in 86ms.Solution:The three squares in the set none of them found were: 36, 841, 9025.There are only 4 possible sets of squares:

Dick found set [1]. Tom and Harry found sets [3] and [4]. Leaving [2] as the set none of them found.