Problem 24 · 2021 Math Kangaroo
Stretch
Logic & Word Problems
casework
Stan has five toys: a ball, a set of blocks, a game, a puzzle and a car. He puts each toy on a different shelf of the bookcase (shelf 1 at the bottom up to shelf 5 at the top). The ball is higher than the blocks and lower than the car. The game is directly above the ball. On which shelf can the puzzle not be placed?
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Answer: C — 3
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Hint 1 of 3
The ball is the key: many clues are about where the ball sits.
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Hint 2 of 3
The game sits right on top of the ball, with the blocks below the ball and the car above it.
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Hint 3 of 3
Try each possible shelf for the ball and see where the puzzle is allowed to land.
Show solution
Approach: test the ball's shelf and rule one out
- If the ball is on shelf 2: blocks on 1, game on 3, and the car and puzzle take shelves 4 and 5 in some order — puzzle is on 4 or 5.
- If the ball is on shelf 3: game on 4, car on 5, and the blocks and puzzle take shelves 1 and 2 — puzzle is on 1 or 2.
- (The ball can not be on 1, with nothing below it, or on 4, leaving no room for the car above the game.)
- So the puzzle can land on 1, 2, 4 or 5, but never on shelf 3.
Mark:
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