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South African Mathematics Olympiad First Round

South Africa counting and probability

Problem

A palindrome is a whole number that reads the same forwards and backwards (e.g. ). How many -digit palindromes are there? (A) (B) (C) (D) (E)
Solution
There are ways to select the nonzero hundreds' digit, then way to select the units' digit (same as the hundreds' digit), and then ways to select the tens' digit. Hence there are three-digit palindromes.
Final answer
B

Techniques

Enumeration with symmetry