## 46. Math Puzzle $3 / 69$

Write down a three-digit number and subtract the number with the reversed digit order. Divide the result by the difference between the 1st and 3rd digit of the original number, then divide by 11 again. If you now take the square root, the result is always 3. This is a neat trick to amaze your friends.

Find out why it works with three-digit numbers!
Representation of an arbitrary three-digit number: $100a + 10b + c$ reversed sequence: $100c + 10b + a$

Difference: $100(a - c) + (c - a) = 99(a - c)$; $a - c$ is the difference between the first and last digit of the original number; dividing by this, one gets 99. And further $99 \div 11 = 9$ and $\sqrt{9} = 3$.

The trick lies in the fact that the unknown digit $b$ falls out through subtraction and by dividing by $(a - c)$, the digits $a$ and $c$ also fall out.