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Dutch Mathematical Olympiad

Number theory Difficulty 4.7 AIME Find the answer Netherlands

The crab of a positive integer is the number you get when you write down its digits in reverse order. For example, the crab of $8267$ equals $7628$ and the crab of $15620$ equals $2651$ (because the leading zero is always dropped).
What is the smallest positive integer $n$ such that $n$ minus the crab of $n$ equals $12345678$ ?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

$20406080$

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