Sum and difference puzzles, step by step

Two numbers add up to 20.

The question

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
71=6
7+1=8
8·6
  1. The question gives two facts and no numbers: they add to 14, and one is 2 more than the other. Everything below comes out of those two.
  2. Split the total evenly first. Half of 14 is 7, so 7 and 7 add up to exactly the right amount. That part is already correct, and it is where every answer to this kind of question starts.
  3. But those two are the SAME, and the question says one is 2 more than the other. So the even split is the right total with the wrong gap — it needs adjusting, not replacing.
  4. Move half the difference across. Half of 2 is 1: give it to one and take it from the other. Moving the WHOLE difference is the usual slip, and it opens a gap of 4.
  5. Check both facts, which is what makes this answer safe: 6 + 8 = 14, and 8 − 6 = 2.

How it works.

  1. 01

    The question gives two facts and no numbers: they add to 14, and one is 2 more than the other. Everything below comes out of those two.

  2. 02

    Split the total evenly first. Half of 14 is 7, so 7 and 7 add up to exactly the right amount. That part is already correct, and it is where every answer to this kind of question starts.

  3. 03

    But those two are the SAME, and the question says one is 2 more than the other. So the even split is the right total with the wrong gap — it needs adjusting, not replacing.

  4. 04

    Move half the difference across. Half of 2 is 1: give it to one and take it from the other. Moving the WHOLE difference is the usual slip, and it opens a gap of 4.

  5. 05

    Check both facts, which is what makes this answer safe: 6 + 8 = 14, and 8 − 6 = 2.