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Divisible Palindrome

Age 14 to 16 Short
Challenge Level

Answer: 5775

Multiple of 15 $\Rightarrow$ multiple of 5 so ends in 5 or 0
0 __ __ 0 not 4 digits
5 __ __ 5

5 + __ + __ + 5 a multiple of 3
Largest possible
5 + 9 + 9 + 5 = 28 no
5 + 8 + 8 + 5 = 26 no
5 + 7 + 7 + 5 = 24 yes


This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.
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