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MathNet 2023-part-01 — 191 problems (EN–VI) Question 21

Math Olympiad Vault · MathNet 2023-part-01 — 191 problems (EN–VI)

Question 21

A number is said to be an *almost palindrome* if it is possible to place a nonzero digit to its left so a palindrome is obtained, that is, a number that reads the same from left to right as from right to left. For instance, $2023$ is an almost palindrome, because we can place the digit $3$ to its left to obtain the number $32023$, which is a palindrome. How many six-digit numbers are almost palindromes and multiples of $9$?