Click here for the Problem Extension Worksheet version of the Problems of the Week.
Click here for an MS Word version of the Problems of the Week.
Click here for the Canadian Problem Extension Worksheet version of the Problems of the Week.
Click here for a Canadian MS Word version of the Problems of the Week.

Lower Elementary:
Question: A protocol droid and a utility droid are both trying to reach an escape pod so that they can get away from an evil imperial spacecraft. The protocol droid walks at a speed of 2 mph. The utility droid rolls at a speed of 5 mph. If they start from the same place, then which one will reach the escape pod first? How can you tell?
Answer: the utility droid
Solution: The faster droid will reach the escape pod first. Since 5 is more than 2, we can tell that 5 mph is faster than 2 mph. So, since the utility droid rolls at a speed of 5 mph, it will reach the escape pod first.

Upper Elementary:
Question: Dejarik is a game played on a circular board. The game is for 2 players, and each player starts the game with 4 game pieces on the board. Each game piece takes up a single space on the board, which has 25 spaces in total. What percentage of the spaces are occupied if both players have all their game pieces in play?
Answer: 32%
Solution: If each player has 4 pieces on the board, then there are 4 × 2 = 8 pieces on the board in total. Since there are 25 spaces on the board, 8/25 of the spaces are occupied. We can turn the fraction into a percent by multiplying both the numerator and denominator by 4, since percentages are out of 100: 8/25 × 4/4 = 32/100 = 32%.

Middle School:
Question: A smuggler’s starship navigates a shortcut through space to make the Kessel Run in 12 parsecs. The usual Kessel Run smuggling route is 18 parsecs. If a parsec is 3.26 light-years and a light-year is 5.88 trillion miles, then by how many trillions of miles does the smuggler shorten the Kessel Run? Round your answer to the nearest trillion miles.
Answer: 115 trillion miles
Solution: Since the usual Kessel Run smuggling route is 18 parsecs and the smuggler’s starship makes it in 12 parsecs, the smuggler shortens the Kessel Run by 18 – 12 = 6 parsecs. Next, we convert 6 parsecs to trillions of miles by multiplying by the conversion rates: 6 parsecs × 3.26 light-years per parsec × 5.88 trillion miles per light year ≈ 115 trillion miles.

Algebra and Up:
Question: A space knight swings her laser sword in a full circle around her body. The laser sword’s energy blade is 3 feet in length. The space knight holds the laser sword so that the blade emits from the hilt 4 feet from the center of the circle. Find the area in which the laser sword’s blade slices through the air.
Answer: 33π square feet
Solution: To find the area in which the blade slices through the air, we find the area of a circle whose radius is 3 + 4 = 7 feet, then subtract the area of a circle whose radius is 4 feet for the space inside the circle where the laser sword’s blade doesn’t touch. The area of the full circle is πr2 = π(7)2 = 49π, and the area of the circle inside is π(4)2 = 16π, so the area inside is 49π – 16π = 33π square feet.