Six Straight Cuts of a Pizza
The problem
What is the largest number of pieces you can divide a round pizza into using exactly six straight cuts with a long knife? You may not stack or move the pieces.
- Each cut is a single straight line across the whole pizza.
- Pieces stay in place between cuts; no stacking or rearranging.
Take a minute
Reveal hint 1
The -th cut adds as many new pieces as the number of existing regions it passes through.
Reveal hint 2
To maximise that number, the new line must cross all previous lines at distinct interior points.
Solution
Answer pieces.
Derivation
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Relate pieces to new crossings.
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Build the recurrence.
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Confirm the choice is achievable.
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Evaluate at .
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Sanity-check small cases.