# Problem Solving (Misc.)

## It's Moving Day

Jessie and Marcus are moving from their apartment to a new condominium. Marcus is responsible for moving all his belongings and the living room furniture, while Jessie is responsible for moving all the kitchen items, including the dining table and chairs, and his personal belongings.

## The Day That Goes on Forever

March 14 has been dubbed Pi Day. That’s because March 14 is often written 3/14, and a decimal approximation of pi is 3.14. But that’s only if you use decimals and our style of writing dates. In some countries, it’s customary to list the date first followed by the month; for example, March 14 would be 14-3 in some places. Consequently, some places celebrate Pi Approximation Day on July 22, because that date can be written as 22-7, and a fractional approximation of pi is 22/7. What percentage of the year occurs between Pi Day and Pi Approximation Day?

## Odds and Evens

The sum of any four consecutive odd integers is a multiple of eight. For example, 1 + 3 + 5 + 7 = 16 and 5 + 7 + 9 + 11 = 32. What is the product of the greatest and least of four consecutive odd integers whose sum is 64?

## Preparing for State

In just a few days, the 2019 MATHCOUNTS State Competitions will begin, so let’s look back at some of the 2018 State Sprint round problems and solve them in preparation.

## MATHCOUNTS Valentine

On some graph paper, graph the following segments:

*y* = *x*, for 0 ≤ *x* ≤ 2*y* = 2*x* − 2, for 2 ≤ *x* ≤ 3*x* = 3, for 4 ≤ *y* ≤ 6*y* = −*x* + 9, for 2 ≤ *x* ≤ 3*y* = 7, for 1 ≤ *x* ≤ 2*y* = *x* + 6, for 0 ≤ *x* ≤ 1

Now reflect each of the segments over the *y*-axis. What popular shape have you drawn?

## Martin Luther King, Jr. Day

Dr. Martin Luther King, Jr., a civil rights activist whose passion and leadership led to great cultural changes in America, was born on January 15, 1929. On November 2, 1983, President Ronald Reagan signed a bill to create a federal holiday honoring Dr. King. The national holiday celebrating the birth of Dr. King was first observed on January 20, 1986. Every year since, Martin Luther King, Jr. Day has been observed on the third Monday of January.

What is the earliest date in January that Martin Luther King, Jr. Day can occur?

## Shaping Up

Jayden started a new exercise program that includes running, cycling, yoga and aerobics. The chart shows how many calories Jayden burns by doing these exercises. Use this data to answer the questions that follow.

## Gift Exchange

Sam, Pam, Ken and Jen are exchanging gifts for the holiday. Each name is written on a slip of paper and placed in a bowl. Sam is the first to randomly select a name from the bowl. What is the probability that Sam selects his own name? Express your answer as a common fraction.

## Geometry of Gift Giving

Vanessa bought some round holiday dessert plates to give as a gift to her friend. However, the store only had 5 of the 8 plates she wanted. (All of the plates are the same.) The stack of five plates measured 1.5 inches tall, and when two plates were removed from the stack the remaining stack of three plates had a height of 1 inch. When Vanessa finally has all 8 of the plates she wants, how tall will the stack of 8 plates be, in inches? Express your answer as a decimal to the nearest hundredth.

## Counting Cookies

Santiago baked gingerbread cookies in the shapes of children. He gave each gingerbread boy and girl eyes made from chocolate covered candies in one of four different colors, a nose made from a butterscotch chip, toffee chip or peanut butter chip, and a mouth made from a piece of red licorice. Santiago then gave each gingerbread boy and girl buttons made from gum drops in one of four different flavors. For the final detail, he gave each gingerbread boy a blue bow tie, and each gingerbread girl a red hair bow.