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Ten to five (Posted on 2018-07-30)

You are given a set of 10 numbers that represent all possible pairwise sums of certain five numbers.

Devise a strategy to find the original five numbers.

Provide a numerical example.

No Solution Yet Submitted by Ady TZIDON

Rating: 3.0000 (1 votes)

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re(2): Corrected solution (spoiler)

| Comment 4 of 7 |

Well, just to be clear, order the partial sums, with w1 the smallest and w10 the largest.

Let S = their sum divided by 4.

Then

a3 = S - w1 - w10

a5 = w9 - a3

a4 = w10 - a5

a1 = w2 - a3

a2 = w1 - a1

Edited on August 1, 2018, 10:49 am

Posted by Steve Herman on 2018-07-30 15:39:41

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