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no of 10-digit sequences

Source: (2021-) 2022 XV 15th Dürer Math Competition Finals Day 2 E+1

December 12, 2022
Digitsnumber theory

Problem Statement

How many 1010-digit sequences are there, made up of 11 four, 22 threes, 33 twos, and 44 ones, in which there is a two in between any two ones, a three in between any two twos, and a four in between any two threes?