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There are three boxes, one blue, one white and one red, and

8

balls. Each of the balls has a number from

1

8

written on it, without repetitions. The

8

balls are distributed in the boxes, so that there are at least two balls in each box. Then, in each box, add up all the numbers written on the balls it contains. The three outcomes are called the blue sum, the white sum, and the red sum, depending on the color of the corresponding box. Find all possible distributions of the balls such that the red sum equals twice the blue sum, and the red sum minus the white sum equals the white sum minus the blue sum.

Problem Statement