# Advent calendar 2019

## 17 December

Eve picks a three digit number then reverses its digits to make a second number. The second number is larger than her original number.

Eve adds her two numbers together; the result is 584. What was Eve's original number?

#### Show answer

#### Hide answer

For the first and last digits of the result to be different, there must be a 1 carried from the middle column. Therefore the middle digit of Eve's number is 9.
Eve's number could be 292 or 193, but it cannot be the first as reversing this is not larger than her original number, so here number is **193**.