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10000 ten-digit numbers divisible by 7, by reordering their digits

Source: Czech And Slovak Mathematical Olympiad, Round III, Category A 1995 p4

February 20, 2020
Digitsnumber theorydivisible

Problem Statement

Do there exist 1000010000 ten-digit numbers divisible by 77, all of which can be obtained from one another by a reordering of their digits?