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jmc

counting and probability junior

Problem

Find the total number of four-digit palindromes. (Recall that a palindrome is a nonnegative sequence of digits which reads the same forwards and backwards, such as 1331. Zero cannot be the first digit.)
Solution
In a four-digit palindrome, the first digit is the same as the last, and the second digit is the same as the third digit. There are 9 options for the first/last digit (1 through 9 -- the first digit cannot be 0), and there are 10 options for the second/third digit (0 through 9). This gives us four-digit palindromes.
Final answer
90