The smudged sum
The question
This sum was photocopied badly and two digits came out blank: 4■ + ■9 = 67.
What were the two numbers?
The ten the ones column sends across
4■+■9=67
8+9=17
4+1=5
without the ten:29
48+19=67
- Two digits are covered. Start with the ones column.
- The ones column settles on its own: something and 9 has to end in 7, and 8 + 9 = 17. So the first covered digit is 8.
- But 17 does not fit in one column. A ten goes across, so the tens column starts at 4 + 1 = 5.
- Forget that ten and you would get 2 — ten too many.
- With it, the tens column is 5 + 1 = 6, so the other covered digit is 1: the two numbers are 48 and 19.
How it works.
- 01
Two digits are covered. Start with the ones column.
- 02
The ones column settles on its own: something and 9 has to end in 7, and 8 + 9 = 17. So the first covered digit is 8.
- 03
But 17 does not fit in one column. A ten goes across, so the tens column starts at 4 + 1 = 5.
- 04
Forget that ten and you would get 2 — ten too many.
- 05
With it, the tens column is 5 + 1 = 6, so the other covered digit is 1: the two numbers are 48 and 19.