Problem number 24. Stan has 5 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. 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? A-1, B-2, C-3, D-4, E-5. We have a picture of the bookcase with the shelves numbered 1, 2, 3, 4, and 5. And it's always helpful to make a picture, especially if we want to see the order in which we can put certain things. So according to this problem, we can start with the ball. The ball is higher than the blocks. Here's the ball and the blocks have to be somewhere below it. Also, the ball is lower than the car, so the car has to be somewhere above the ball. The next statement tells us that the game is directly above the ball. So the game is right above the ball. That means that on the shelves, these will have to be right next to each other. For example, if the ball is on shelf 2, then the game has to be on shelf 3. Now the problem doesn't give us any direction as to where the puzzle can be, other than telling us how the other things are arranged. So we can try different arrangements and figure out if there's a shelf that will definitely not work for the puzzle. So our first option is to start from the bottom. The blocks could be on shelf 1. The ball and the game are on the next two shelves. After that, we could either put the puzzle on shelf 4, below the car, and the car on shelf 5, or do it the other way and put the puzzle on shelf 5 and the car on shelf 4. So the puzzle could be on shelf 4 or 5. Now if the blocks are on shelf 1, we could put the puzzle on shelf 2. Then the ball could go on shelf 3, the game on shelf 4, and the car on shelf 5. So that arrangement doesn't work. So the puzzle could be on shelf 2. So that's not a shelf that it cannot go on. Also, we could try putting the puzzle on shelf 1, then we get the blocks on shelf 2, and then the ball, the game, and then the car. So we can't put the puzzle on shelf 1. So the only shelf on which the puzzle would never be placed is shelf 3. So the answer is C, 3. With the ball and the game being next to each other, and there always being at least one toy below it and above it, the only way to place them is on shelves 2 and 3, or 3 and 4. So no matter what, one of these toys is on shelf 3. So that is the shelf that we cannot put the puzzle on.

toys arrangement

shelf constraints

ball and game

puzzle placement

logical deduction