# Plane Geometry

## State Countdown

Here are a few of the problems that competitors had to solve as they faced off in head-to-head matches during the 2018 State Countdown Round.

## Happy Pi Day

This Wednesday (3/14) was Pi Day. Here are a few questions in honor of the day.

If Celia ate 1/4 of 2/3 of 1/2 of a pie, what fraction of the whole pie did she eat? Express your answer as a common fraction.

Celia ate (1/4)(2/3)(1/2) =of the whole pie.1/12

## Tangram Geometry

## Happy New Year!

Happy New Year! Now that 2018 is here, let’s have some fun with this number!

What is the last digit of 2018^{2018}?

The units digits of the powers of 2018 are the same as the units digits of the powers of 8, and they form a pattern that repeats every four powers. The pattern of units digits is 8, 4, 2 and 6. Since 2018 is 2 more than a multiple of 4, it follows that the units digit of 2018^{2018}is the second digit in this pattern, which is.4