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MathNet 2012 Question 89

Math Olympiad Vault · MathNet 2012

Question 89

Is it possible to write numbers $1, 2, 3, 4, 5, 6, 7, 8$ at the vertices of an octagon (one number at each vertex) so that the sum of numbers in each three consecutive vertices is greater than:

a) $13$;
b) $11$;
c) $12$?