
## 1. Food from Italy

Italy is the European country that is shaped like a boot.

Many popular dishes have their origin in Italy test
1. ### This is the heading of the problem

These are introductory words meant to be read before the problem statement.

#### Problem 1.1.

[Luigi] How many pieces of pizza are in a typical pizza pie?
1. Remark. [David Faermer] Eight is the most common, in my experience.
• Remark. [Jason Davies] test
• Remark. [Kent] See piece-def for its definition.
• Remark. [Terry] Costco Pizza has 18 slices on average.
•     The following is actually a real mathematics problem.

#### Problem 1.2.

Given a plate of spaghetti with $N$ noodles, suppose you randomly connect each end of a noodle to another end, with all connections equally likely. What is the expected number of loops?
1. Remark. When $N=1$ there is exactly one loop.

When $N=2$ there can be either 1 or 2 loops, with 2 loops occurring 1/3 of the time. So the expected number of loops is $\frac13 2 + \frac23 1 = \frac43$.