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Restrictions on a,b with a+b=999

Source: 2014 SDMO Middle School Problem 3

August 28, 2016

Problem Statement

How many ordered pairs of nonnegative integers (a,b)\left(a,b\right) are there with a+b=999a+b=999 such that each of aa and bb consists of at most two different digits? (These distinct digits need not be the same digits in both aa and bb. For example, we might have a=622a=622 and b=377b=377.)
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