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: Alexis brings 21/2 sandwiches to a picnic. Brett brings twice as many sandwiches as Alexis. How many sandwiches do Alexis and Brett have altogether?
Answer: 71/2 sandwiches
Solution: If Alexis brings 21/2 sandwiches, then Brett brings 21/2 + 21/2 = 5 sandwiches. If we add up Alexis’s sandwiches and Brett’s sandwiches, we get 21/2 + 5 = 71/2 sandwiches.

Upper Elementary:
Question: If Cody has 20 game tokens to spend at the arcade. He spends $2.40 to get 12 more. How much did Cody’s game tokens cost altogether?
Answer: $6.40
Solution: Since Cody spends $2.40 to buy 12 tokens, each token costs $2.40 ÷ 12 = $0.20. Cody has 20 + 12 = 32 tokens altogether, so his game tokens cost $0.20 × 32 = $6.40.

Middle School:
Question: Darla has a number of movies in her collection; 1/4 of the movies are comedies, 1/3 are documentaries, 1/6 are horror movies, and the rest are dramas. The total number of movies in Darla’s collection is between 20 and 30. Exactly how many documentaries does she have?
Answer: 8 documentaries
Solution: Darla can’t own half a movie—that doesn’t make any sense. So, since we know Darla’s movie collection can be divided evenly by 4, 3, and 6, we’re looking for a number between 20 and 30 that is divisible by those three numbers. The only number that fits the bill is 24. So, since 1/3 of 24 is 8, Darla must have 8 documentaries.

Algebra and Up:
Question: A syllogism is a logic puzzle that asks you to draw a conclusion based on the logical values or truth values of a series of statements, like these:

1) I’m thinking of a shape that is concave.
2) All triangles are convex.
3) A shape is convex if and only if it is not concave.

What conclusion can you draw about the shape I’m thinking of based on the statements above?
Answer: I am not thinking of a triangle.
Solution: If we start with the third statement and apply it to the first, we can conclude that I am not thinking of a convex shape. If we know that I’m not thinking of a convex shape, then we can conclude that I cannot possibly thinking of a triangle because that would contradict the second statement—all triangles are convex.