The lazy caterer
The question
A pie is sliced 6 times, every slice a straight line across the whole pie, with no piece moved in between.
What is the greatest number of pieces?
Count cuts and their crossings, do not just double
doubling guess:64
cuts / pairs:615
6+15=21
21+1=22
- 6 straight cuts. The counts so far run 2, 4, so the guess is that it keeps doubling to 64. Let's check.
- Count it properly. Start with 1 whole pie and add one piece per cut, C(6,1) = 6, and one per pair of cuts that cross, C(6,2) = 15.
- Add them: 6 + 15 = 21, and the whole pie makes 21 + 1 = 22. Not 64 — the doubling has broken.
How it works.
- 01
6 straight cuts. The counts so far run 2, 4, so the guess is that it keeps doubling to 64. Let's check.
- 02
Count it properly. Start with 1 whole pie and add one piece per cut, C(6,1) = 6, and one per pair of cuts that cross, C(6,2) = 15.
- 03
Add them: 6 + 15 = 21, and the whole pie makes 21 + 1 = 22. Not 64 — the doubling has broken.