# Problems of the Week

Mar 9, 2020 | High Park

A sunny weekend in Toronto has inspired this week's problems! Can you solve these, Mathletes?

Lower Elementary:
Question: Jack builds a sand castle with 8 different sand molds. The smallest mold holds 11/2 cups of sand. The next mold holds 3 cups of sand. The third mold holds 6 cups of sand, and the fourth holds 12 cups of sand. If the pattern continues, then how much sand does the biggest mold hold?

Upper Elementary:
Question: Aria, Brett, and Chelsea bounce a beach ball between them 100 times. Aria bounces the ball to Brett, Brett bounces the ball to Chelsea, Chelsea bounces the ball to Aria, and the pattern continues. Who bounces the ball the 100th time?

Middle School:
Question: Ava collects 4 more than twice as many sea shells as Ben. Ben collects 1 fewer than half as many as Carla. Carla collects 200 sea shells. How many sea shells does Ava collect?

Algebra and Up:
Question: A circular beach umbrella with an area of 16π square feet casts a circular shadow with a circumference of 16π feet. What is the circumference of an umbrella at the same height that casts a shadow whose area is 256π square feet? (For the purposes of this exercise, pretend umbrellas are flat circles instead of domes.)

...

Lower Elementary:

Question: Jack builds a sand castle with 8 different sand molds. The smallest mold holds 11/2 cups of sand. The next mold holds 3 cups of sand. The third mold holds 6 cups of sand, and the fourth holds 12 cups of sand. If the pattern continues, then how much sand does the biggest mold hold?

Solution: Each mold holds twice as much as the last. So, the fifth holds 12 + 12 = 24 cups. The sixth holds 24 + 24 = 48 cups. The seventh holds 48 + 48 = 96 cups, and the eighth holds 96 + 96 = 192 cups.

Upper Elementary:
Question: Aria, Brett, and Chelsea bounce a beach ball between them 100 times. Aria bounces the ball to Brett, Brett bounces the ball to Chelsea, Chelsea bounces the ball to Aria, and the pattern continues. Who bounces the ball the 100th time?