Y by nmd27082001, mathematicsy, Adventure10, megarnie, HWenslawski, Mango247, ItsBesi
Suppose that the set
has been partitioned into disjoint pairs
(
) so that for all
,
equals
or
. Prove that the sum
ends in the digit
.







![\[ |a_1-b_1|+|a_2-b_2|+\cdots +|a_{999}-b_{999}| \]](http://latex.artofproblemsolving.com/0/4/4/04422a7d2266b92a6b3f215b698f078cda85091f.png)

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