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The sum is a square (Posted on 2016-03-04) Difficulty: 3 of 5
Prove the following identity:

In any partition of the first 2N natural numbers into decreasing and increasing sequences of N members each, the sum of absolute values of the differences of the corresponding members of the two sequences is always N^2.

Source: Savchev, Svetoslav; Andreescu, Titu. Mathematical Miniatures. Washington, D.C.

No Solution Yet Submitted by Ady TZIDON    
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  Subject Author Date
quick wayarmando2016-03-05 06:16:30
Some Thoughtspossible solutionbroll2016-03-05 01:22:05
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