Problem C

Stacking Bowls

Alice has a set of bowls of various sizes. She likes stacking her
bowls upside down. A bowl can be *stacked over* another bowl if
the smaller bowl can be completely enclosed by the larger bowl. This
means the larger bowl can completely hide the smaller bowl.

For the example below, a bowl with a width of \(10\) cm and height \(10\) cm can stack over a bowl with a width of \(5\) cm and a height of \(5\) cm. In turn they can be stacked over by a bowl with a width of \(20\) cm and a height of \(20\) cm. This gives a single stack.

On the other hand, a bowl with a width of \(20\) cm and a height of \(20\) cm cannot be stacked over a bowl of a width of \(25\) cm and a height of \(15\) cm. Also, a bowl with a width of \(25\) cm and a height of \(15\) cm cannot be stacked over a bowl of a width of \(20\) cm and a height of \(20\) cm.

Alice has the following set of bowls and starts stacking them. What is the fewest number of stacks that Alice can have?

**Theme: **Number Sense