A cut along the diameter of a circular paper will obtain 2 equal pieces. How many such cuts along the diameter must be made to obtain 16 smaller pieces of equal size?

1. Determine the relationship between the number of cuts along the diameter and the number of pieces obtained.

Each cut along the diameter passes through the centre of the circle.
$1$ cut produces $2$ pieces.
$2$ cuts produce $4$ pieces.
$3$ cuts produce $6$ pieces.
In general, $n$ cuts produce $2n$ pieces.

2. Calculate the number of cuts required for 16 pieces.

Let $n$ be the number of cuts.
$2n = 16$
$n = 16 \div 2 = 8$