The integers 1, 2, ..., 10 are written on a circle, in any order. Show that there are 3 adjacent numbers whose sum is 17 or greater.

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Copyright © 1996-2018 Alexander Bogomolny
The integers 1, 2, ..., 10 are written on a circle, in any order. Show that there are 3 adjacent numbers whose sum is 17 or greater.

There are 10 triples of adjacent numbers with sums S_{1}, S_{2}, ..., S_{10}. If each is less than 17, they all add up to _{i} are bound to be greater than 16.

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Copyright © 1996-2018 Alexander Bogomolny