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Hidden Palindrome

Problem

A palindrome is a number which reads the same forwards and backwards. For example, the number 232 is a 3-digit palindrome.

Can you find a square 3-digit palindrome, which is also palindromic when divided by 2?


Solution

If it is palindromic when divided by 2, it must be even. For a square number, n2, to be even, n must be even.

Listing even 3-digit squares:
102 = 100, 122 = 144, 142 = 196, 162 = 256,
182 = 324, 202 = 400, 222 = 484, 242 = 576,
262 = 676, 282 = 784, 302 = 900.

The two candidates are 484 and 676, but as 484/2=242 and 676/2=338, the palindrome we seek is 484.

Problem ID: 163 (Apr 2004)     Difficulty: 1 Star

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