# A digit reversal

**Number Theory**Level 3

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 \( 10987654321\).