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2021 Combo Div 1 P3 (Div 2 P7)

Source:

March 2, 2021
combinatorics

Problem Statement

How many permutations of the string 01234560123456 are there such that no contiguous substrings of lengths 1<ℓ<71<\ell<7 have a sum of digits divisible by 77?
Proposed by Srinivasan Sathiamurthy
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