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k white and m black dice, equal sums remainders mod 7, probability

Source: Polish second round 1997 p5

January 19, 2020
probabilitysumsDiceremaindernumber theorycombinatorics

Problem Statement

We have thrown kk white dice and mm black dice. Find the probability that the remainder modulo 77 of the sum of the numbers on the white dice is equal to the remainder modulo 77 of the sum of the numbers on the black dice.