A number is called a palindrome if it reads the same backward as forward.

Question

A number is called a palindrome if it reads the same backward as forward. The number of six digit palindromes which are divisible by 55 is:

Answer: 100

Accepted Answer

A six-digit palindrome has the form $\overline{xyzzyx}$. For divisibility by $55=5	imes11$: divisibility by 5 forces $x=5$ (leading digit can't be 0).

The alternating sum for 11-divisibility, $(5+z+y)-(y+z+5)=0$, is automatically a multiple of 11 for any $y,z$.

So $y,z$ can each be any of $10$ digits: $10	imes10=100$.

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