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MathNet 2022-part-01 — 197 problems (EN–VI) Question 196

Math Olympiad Vault · MathNet 2022-part-01 — 197 problems (EN–VI)

Question 196

We say that a positive integer $k$ is *fair* if the number of $2021$-digit palindromes that are a multiple of $k$ is the same as the number of $2022$-digit palindromes that are a multiple of $k$. Does the set $M = \{1, 2, \dots, 35\}$ contain more numbers that are fair or those that are not fair?

(A palindrome is an integer that reads the same forward and backward.)

(David Hruška)