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# Divisability

-4
53
3
+-291

A $\textit{palindrome}$ is an integer that reads the same forwards and backwards. How many positive 3-digit palindromes are multiples of $3$?

Mar 31, 2020

#1
+210
+1

Here's an interesting way to think about it. For every digit $$a$$ in the palindrome $$aba$$, there are either exactly 3 and occassionally 4 palindromes that you can make that are multiples of 3. See if you figure out why and when that exception happens.

Mar 31, 2020
edited by Impasta  Mar 31, 2020
#2
+1

(111, 141, 171, 222, 252, 282, 303, 333, 363, 393, 414, 444, 474, 525, 555, 585, 606, 636, 666, 696, 717, 747, 777, 828, 858, 888, 909, 939, 969, 999) >>Total = 30 such numbers.

Mar 31, 2020