Sum and difference puzzles
The question
Two baskets hold 14 apples altogether. One basket has 2 more apples than the other.
How many apples are in each basket?
Two numbers from their total and their gap
total:14· gap:2
7and7
gap now:0· gap wanted:2
7−1=6
7+1=8
8·6
- Two numbers add to 14, and one is 2 more than the other.
- Split the total evenly first. Half of 14 is 7, so 7 and 7 add up to the right total.
- But those two are the same, and one should be 2 more. The total is right; the gap is not.
- Move half the difference across. Half of 2 is 1: give it to one and take it from the other — moving the whole 2 would make the gap 4.
- Check both facts: 6 + 8 = 14, and 8 − 6 = 2.
How it works.
- 01
Two numbers add to 14, and one is 2 more than the other.
- 02
Split the total evenly first. Half of 14 is 7, so 7 and 7 add up to the right total.
- 03
But those two are the same, and one should be 2 more. The total is right; the gap is not.
- 04
Move half the difference across. Half of 2 is 1: give it to one and take it from the other — moving the whole 2 would make the gap 4.
- 05
Check both facts: 6 + 8 = 14, and 8 − 6 = 2.