An Odd Request

A puzzle by Polish mathematician Paul Vaderlind:

Is it possible to arrange 25 whole numbers (not necessarily all different) so that the sum of any three successive terms is even but the sum of all 25 is odd?

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Yes. Let E stand for an even number and O for an odd and consider the sequence OEO OEO OEO OEO OEO OEO OEO OEO O. Any group of three consecutive terms contains one even number and two odd, giving an even sum. But 17 of the numbers are odd, so the sum of the whole group is odd. From Vaderlind’s excellent 2002 book The Inquisitive Problem Solver.

May 18, 2024May 17, 2024 | Puzzles