If you apply one straight cut to a pancake, pretty clearly you’ll get 2 pieces. With two cuts, the most you can get is 4. What’s the greatest number you can produce with three cuts? If the cuts meet neatly in the center, you’ll get 6 pieces, but if you’re artfully sloppy you can make 7 (above).
Charmingly, this leads us into the “lazy caterer’s sequence” — the maximum number of pieces you can produce with n straight cuts:1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191, 211, …
Generally it turns out that the maximum number for n cuts is given by the formula
each number equals 1 plus a triangular number.
A related question is the pancake flipping problem. You’re presented with a spatula and an untidy stack of pancakes of varying…
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