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any 6 noumbers from a 6x6 ray have equal product

Source: 2001 Swedish Mathematical Competition p1

March 21, 2021
algebraProduct

Problem Statement

Show that if we take any six numbers from the following array, one from each row and column, then the product is always the same:
4 6 10 14 22 26 6 9 15 21 33 39 10 15 25 35 55 65 16 24 40 56 88 104 18 27 45 63 99 117 20 30 50 70 110 130