Take any three-digit positive integer, reverse its digits, and subtract. The difference is divisible by 11. Take any three-digit positive integer, reverse its digits, and subtract. For example, 742 − 247 =
495. The difference is divisible by 11. Prove that this must happen for all three-digit numbers abc

\begin{align}
x &= 100a + 10b + c \quad &\text{Any three digit number can be expressed in this form}\\
y &= 100c + 10b +a \quad &\text{This is the number once the digits are reversed}\\
x-y &= 100a - a + 10b -10b +c -100c = 99a-99c\\
x-y &=11 \cdot(9a-9c)
\end{align}
