Henry Ernest Dudeney/Modern Puzzles/106 - Dissecting the Moon/Solution

Modern Puzzles by Henry Ernest Dudeney: $106$

Dissecting the Moon

In how large a number of pieces can this crescent moon be cut with five straight cuts of the knife?

The pieces may not be piled or shifted after a cut.

Solution

As many as $21$ pieces:

The maximum number of pieces a crescent can be cut into by $n$ cuts is $\dfrac {n^2 + 3 n} 2 + 1$.

For a circle, you can only make $\dfrac {n^2 + n} 2 + 1$ pieces.

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Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Solutions: $106$. -- Dissecting the Moon
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $302$. Dissecting the Moon