The minimum of maximum

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Consider all ordered 5-tuples of positive integers ( a , b , c , d , e ) (a,b,c,d,e) such that a + b + c + d + e = 2014 a+b+c+d+e=2014 . Let M M be the maximum of the numbers a + b , b + c , c + d , d + e a+b, b+c, c+d, d+e . Over all such 5-tuples, what is the minimum value of M M ?


The answer is 807.

Antony Diaz by Antony Diaz , 25, Canada

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