This paper considers the problem of choosingn numbers in the unit interval in such a way that their products in pairs are distributed as evenly as possible. Specifically, it is desired (i) to maximize the minimum diff...
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This paper considers the problem of choosingn numbers in the unit interval in such a way that their products in pairs are distributed as evenly as possible. Specifically, it is desired (i) to maximize the minimum difference between successive products or (ii) to minimize the maximum difference between successive products. These problems are solved for the casesn=1, 2, 3. For generaln, the problems are solved under certain additional restrictions, and the limiting behavior for largen is determined. The situation for generaln is investigated further by posing and solving a continuous analogue of the discrete problem. This leads to a heuristic method of determining the optimum order of products in the general case.
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