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

by : $106$

 * Dissecting the Moon

Solution
As many as $21$ pieces:


 * Dudeney-Modern-Puzzles-106-solution.png

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.