# A digit reversal

Let $$S$$ be the number obtained by writing all the numbers from 1 to 100 in order, and removing the spaces in between. Let $$T$$ be the number obtained by writing all the numbers from 1 to 100 in reverse order and removing the spaces in between.

What is the remainder when $$T^2 - S^2$$ is divided by $$1000$$?

Details and assumptions

The number obtained by writing all the numbers from 1 to 10 in reverse order and removing the spaces in between, is $$10987654321$$.

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