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Divisible Palindrome

Stage: 3 and 4 Short Challenge Level: Challenge Level:2 Challenge Level:2

What is the sum of the digits of the largest 4-digit palindromic number which is divisible by 15? [Palindromic numbers read the same backwards and forwards, e.g. 7227 or 10101.]

If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.
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