Independence Day 2017

To celebrate Independence Day, students attending a summer camp painted the American flag mural, show here, with the dimensions in centimeters.  If the area of each of the stars is 22.2 cm2, how many square centimeters of the flag is painted blue?

 

Ice Cream Shoppe

Small Town Ice Cream Shoppe carries five kinds of ice cream: vanilla, chocolate, strawberry, lemon custard, and caramel swirl. They also have three types of toppings: sprinkles, chopped nuts, and hot fudge. A “Shoppe Supreme” consists of three scoops of ice cream, not necessarily distinct flavors, and three scoops of toppings, also not necessarily distinct. The ice cream is always scooped before the toppings are added, in how many distinct ways can a Shoppe Supreme be assembled at Small Town Ice Cream Shoppe?

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.

 

Pool Maintenance

Every Memorial Day weekend, Jay’s family fills up their pool for the summer season. Since Jay’s favorite subject is math, he decided to calculate how long it will take for the pool to fill. Jay times the water exiting their garden hose and figures out it’s flowing at a rate of 10 gallons per minute. Their rectangular pool is 16 feet long and 8 feet wide, and they fill the pool till the water is 4 feet deep. The last thing Jay needs for his calculation is the conversion between gallons and cubic feet. He searches on the internet and finds that 1 gallon is equal to 2/15 of a cubic foot.

2017 National Competition

Last week the National Competition concluded, and Luke Robitaille from Texas became the 2017 MATHCOUNTS National Champion. Let’s look at some of the problems he had to solve on the way to the top!

What is the maximum possible absolute difference between a two-digit integer and the two-digit integer resulting when the digits are reversed?

We want the largest possible two-digit integer and the smallest possible two-digit integer that have their digits reversed. These are 91 and 19. The difference is 91 – 19 = 72.

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?

National Competition

On Sunday, May 14th, 224 of the nation’s smartest middle-school math minds will be in Orlando, FL for the 2017 Raytheon MATHCOUNTS National Competition. The stakes are high, and the problems will be tough. Here are a few sprint round problems national competitors solved in 2016.

Spring Festival

Originally posted: 4/2/12

It’s time for the Spring Festival. This year 63 children will be attending, and each child will receive a basket that includes 2 candy-filled Easter eggs. If the candy-filled eggs are sold by the dozen like real eggs, what is the minimum number of dozens needed for the children’s baskets?

NCAA Final Four

And then there were four: South Carolina in the East bracket, Gonzaga in the West bracket, Oregon in the Midwest bracket and North Carolina in the South bracket. These four teams have earned a coveted spot in the arena known as the Final Four. There were 64 teams (not including play-in games) who entered the NCAA Tournament – 16 teams in each of the four brackets. The tournament is a single elimination, meaning each game played eliminates one team. How many games had to be played to determine the Final Four?

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 is 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?

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