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6 Straight Cuts Across a Pancake: What's the Maximum Number of Pieces?
What is the maximum number of pieces you can get by making six straight cuts across a circular disk (each line crossing all the others)?
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What is the answer to the 6 straight cuts on a pancake riddle?
The maximum is 22 pieces. Using the lazy caterer formula 1 + n + C(n,2) with n = 6 gives 1 + 6 + 15 = 22.
How does the lazy caterer formula work?
Each new cut adds as many pieces as the number of cuts it crosses, plus one. The closed form is 1 + n + n(n-1)/2, so 6 cuts give 22 pieces.
Why isn't the answer 64 or some power of 2?
Straight cuts only double the pieces up to 2 cuts. After that each cut adds n new pieces, not double, so 6 cuts top out at 22, not 64.