Brain Teasers
If Your Friend Jumped Off a Cliff, Would You Know Her Height?
Logic-Grid
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One Wednesday last August (I forget the exact date), the Froopaloop River was teeming with swimmers. Some of them just relaxed, but many of them jumped from one of five cliffs into the water below. Lots of people jumped from the 3-foot cliff or the 6-foot cliff, a few braver souls jumped from the 12-foot cliff or the 24-foot cliff, but only one daredevil jumped from the 30-foot cliff.
This teaser concerns five women who went to the river together that day. Each one has a different name, wore a different-coloured bathing suit, and stands at a different height (5'2, 5'4, 5'6, 5'8, or 5'10). Finally each woman jumped off only one cliff for the entire trip, and each one jumped off a different cliff. (Yes, one of them was the daredevil I mentioned in the previous paragraph.)
Here are some facts:
1. The cliff from which the woman in the white one-piece jumped is higher than that from which the second-tallest woman jumped, but lower than at least two other cliffs.
2. Lisa didn't wear blue.
3. The tallest woman's cliff is 6 feet higher than that from which the woman in the pink one-piece jumped. The lady in pink is 2 inches shorter than Martha.
4. Pansy's cliff is twice as high as that from which the one in the red bikini jumped. Ophelia's is twice as high as that from which the second-shortest woman jumped.
5. The height of the shortest woman's cliff plus the height of that from which the woman in the yellow one-piece jumped equals the height of Pansy's cliff plus the height of that from which the woman in the blue bikini jumped. The shortest woman didn't wear blue.
The question is, how tall is the woman named Nora?
This teaser concerns five women who went to the river together that day. Each one has a different name, wore a different-coloured bathing suit, and stands at a different height (5'2, 5'4, 5'6, 5'8, or 5'10). Finally each woman jumped off only one cliff for the entire trip, and each one jumped off a different cliff. (Yes, one of them was the daredevil I mentioned in the previous paragraph.)
Here are some facts:
1. The cliff from which the woman in the white one-piece jumped is higher than that from which the second-tallest woman jumped, but lower than at least two other cliffs.
2. Lisa didn't wear blue.
3. The tallest woman's cliff is 6 feet higher than that from which the woman in the pink one-piece jumped. The lady in pink is 2 inches shorter than Martha.
4. Pansy's cliff is twice as high as that from which the one in the red bikini jumped. Ophelia's is twice as high as that from which the second-shortest woman jumped.
5. The height of the shortest woman's cliff plus the height of that from which the woman in the yellow one-piece jumped equals the height of Pansy's cliff plus the height of that from which the woman in the blue bikini jumped. The shortest woman didn't wear blue.
The question is, how tall is the woman named Nora?
Hint
If you get stuck, try and see what will happen if the tallest woman jumps from the 12-foot cliff.Answer
Nora is a whopping 5'10.The woman in blue obviously didn't wear yellow, and fact 5 tells us that she's not the shortest woman. Therefore, the two sides of the equation in fact 5 must have different addends, i.e. cliff heights. Each pair of cliff heights, including doubling one cliff height, adds to a different sum, except 6+30 and 12+24. This gives us two possible scenarios:
1. Shortest and yellow jumped 6' and 30' in some order, and Pansy and blue jumped 12' and 24' in some order.
2. Shortest and yellow jumped 12' and 24' in some order, and Pansy and blue jumped 6' and 30' in some order.
In both scenarios, the woman who jumped 3' cannot wear yellow or blue. Since that cliff is the lowest, fact 1 tells us she didn't wear white, and since there is no 9' cliff, fact 3 tells us she didn't wear pink, leaving only red. Then, from fact 4, Pansy jumped 6', which means that scenario 2 is true, blue jumped 30', and shortest and yellow jumped 12' and 24', in some order.
Since there is no 18' cliff, fact 3 tells us that the tallest woman jumped 12' or 30'. If she jumped 12', previous reasoning tells us that she wore yellow and the shortest woman jumped 24'. Fact 3 tells us that the one who jumped 6' wore pink, which leaves the one in white to jump 24'. But from fact 1, this cannot work, which means that the tallest woman jumped 30'.
Continuing in this manner, we can determine that there is only one possible solution:
5'2 Ophelia jumped 24' in her pink one-piece.
5'4 Martha jumped 12' in her yellow one-piece.
5'6 Pansy jumped 6' in her white one-piece.
5'8 Lisa jumped 3' in her red bikini.
5'10 Nora was the daredevil who jumped 30' in her blue bikini.
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