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Four squares

I have before me five two-digit numbers, with no leading zeros. All the digits are different and none of the numbers is prime. The sum of the five numbers is a perfect square. If I remove one of the numbers, the sum of the remaining four is also a perfect square. If I remove another number, the sum of the remaining three is again a perfect square, and if I remove a third number, the sum of the last two is again a perfect square.

What are my five numbers?

WIN £15 will be awarded to the sender of the first correct answer opened on Wednesday 17 April. The Editor’s decision is final. Please send entries to Enigma 1741, New ÐÓ°ÉÔ­´´, Lacon House, 84 Theobald’s Road, London WC1X 8NS, or to enigma@newscientist.com (please include your postal address).

Answer to 1735 A pile of coloured cubes: 24 cubes are in the leftover pile

The winner Bernard Ambrose of Little Melton, Norfolk, UK