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Not deducible

Harry and Tom have each found a 4-digit perfect square, a 3-digit perfect cube and a 3-digit triangular number that use 10 different digits, but with no leading zero. A triangular number is one that fits the formula n(n+1)/2, such as 1, 3, 6, 10, 15.

Even if I told you Harry’s triangular number you would not be able to deduce with certainty which perfect square he has found. Even if I told you Tom’s perfect square you would not be able to deduce with certainty which triangular number he has found.

What are (a) Harry’s triangular number, and (b) Tom’s perfect square?

WIN £15 will be awarded to the sender of the first correct answer opened on Wednesday 8 August. The Editor’s decision is final. Please send entries to Enigma 1705, New Å®ÉúСÊÓƵ, Lacon House, 84 Theobald’s Road, London WC1X 8NS, or to enigma@newscientist.com (please include your postal address).

Answer to 1699 Double time: 4 hours 36 minutes 55 seconds

The winner Alan Hands of Redditch, Worcestershire, UK