**From New Scientist #2385, 8th March 2003** [link]

Harry, Tom and I have been challenged to find a solution to the following statement in which digits have been consistently replaced by capital letters, different letters being used for different digits and no number starting with a zero:

FOUR is a perfect square, FIVE is a Fibonacci number, SIX is a semi-prime.

In the sequence of Fibonacci numbers the first two terms are 1 and 1, and every other term is the sum of the previous two terms. A semi-prime is the product of two prime numbers.

Harry, Tom and I have each found a different solution. None of the numbers used in my solution appears in either of theirs.

What are the numbers represented by FOUR, FIVE and SIX (in this order) in my solution?

[enigma1229]

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This Python program runs in 42ms. We could prune the candidate lists of numbers by noting that they cannot contain repeated digits.

Solution:FOUR=1024, FIVE=1597, SIX=358.Harry and Tom’s numbers are (FOUR=2601, FIVE=2584, SIX=753) and (FOUR=2916, FIVE=2584, SIX=753) – which have the same values for FIVE and SIX – but we don’t know who found which set.