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#68 Another 2025 puzzle

Set by Peter Rowlett

The square root of 2025 is 45. The divisors of 45 (apart from 45 itself) are 1, 3, 5, 9 and 15. The product of these numbers is 2025.

The last year that was a square number was 1936. Does 1936 also have this property?

What is the smallest square number with this property? Does it work for all square numbers?

Solution next week

#67 Pandigital sums

Solution

There are four solutions to ABCD + EF = GHIJ where GHIJ = 2034. 1956 + 78, 1958 + 76, 1976 + 58 and 1978 + 56 all work.

There are 16 solutions to ABC + DEF = GHIJ where GHIJ = 1089.

The solution to ABC + DEF = GHIJ with A < B < C < D < E < F is 246 + 789 = 1035.