# The minimum of maximum

Level pending

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

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