MathDB

3

Part of 2020 Regional Olympiad of Mexico Northeast

Problems(1)

no of permutations satisfy that none of s_1,...,s_{100} is divisiblle by 3

Source: Mathematics Regional Olympiad of Mexico Northeast 2020 P3

9/7/2022
A permutation of the integers 2020,2021,...,2118,21192020, 2021,...,2118, 2119 is a list a1,a2,a3,...,a100a_1,a_2,a_3,...,a_{100} where each one of the numbers appears exactly once. For each permutation we define the partial sums. s1=a1s_1=a_1 s2=a1+a2s_2=a_1+a_2 s3=a1+a2+a3s_3=a_1+a_2+a_3 ...... s100=a1+a2+...+a100s_{100}=a_1+a_2+...+a_{100} How many of these permutations satisfy that none of the numbers s1,...,s100s_1,...,s_{100} is divisible by 33?
permutationscombinatorics