## 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.

If the top surface of a particular slice of pie is a sector of a circle with a vertex angle measuring 20 degrees and the length of the arc is π units, what is the circumference of the top surface of the whole pie? Express your answer in terms of π.

## 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

## Happy Flag Day!

A stand at a local parade is selling flags for observers to wave. The small flags each cost 2/3 the price of each large flags and each flag costs a whole number of dollars. If Frida bought 5 flags and spent $24.00, how much do each of the small flags cost in dollars?

Because the numbers are small, guess and check may be used to solve this one. If the large flags each cost $6 dollars, the small flags would each cost $4. To make sure this is feasible: $4 + $4 + $4 + $6 + $6 = $.24

## Mother's Day

Anna asked six of her friends for the age in years of their mothers, shown in the table below. What is the positive difference between their mean and median age?

## Countdown to Nationals

We are officially two weeks away from this year’s MATHCOUNTS National Competition Countdown Round! The top 12 competitors in the country will go head to head to answer questions in 45 seconds or less. Let’s look at some questions they answered last year. How fast can you solve them?

To make a compact disc, a machine creates a circular disc with diameter 120 mm and then punches a center hole with diameter 15 mm. When the hole is punched, what fraction of the original area is removed? Express your answer as a common fraction.