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An athlete has six trophies to place on an empty three-shelf display case. The six trophies are bowling trophies F, G, and H and tennis trophies J, K, and L. The three shelves of the display case are labelled 1 to 3 from top to bottom. Any of the shelves can remain empty. The athlete's placement of trophies must conform to the following conditions:
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J and L cannot be on the same shelf
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F must be on the shelf immediately above the shelf that L is on.
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No single shelf can hold all three bowling trophies
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K cannot be on Shelf 2
Question 1
If G and H are on Shelf 2, which of the following must be true?
1. K is on Shelf 1.
2. L is on Shelf 2.
3. J is on Shelf 3.
4. G and J are on the same shelf.
5. F and K are on the same shelf.
Question 2
If no tennis trophies are on Shelf 3, which pair of trophies must be on the same shelf?
1. F and G
2. L and H
3. L and G
4. K and J
5. G and H
Question 3
If J is on shelf 2, which of the following must also be on Shelf 2?
1. K
2. G
3. F
4. L
5. H
Question 4
If Shelf 1 remains empty, which of the following must be FALSE?
1. H and F are on the same shelf.
2. There are exactly three trophies on Shelf 2.
3. G and H are on the same shelf.
4. There are exactly two trophies on Shelf 3.
5. G and K are on the same shelf.
Question 5
If L and G are on the same shelf, and if one of the shelves remains empty, which of the following must be true?