# 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.