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Answers to the previous problems are down below. Just scroll down for them. Scroll carefully because the questions come up first, so if you want to try them before you see the answer, don't scroll all the way down.

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The Worm's Travels

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There are three books, each one inch thick. They stand side by side in order -- Volumes I, II, and III. A book worm starts outside the front cover of Volume I and eats its way through to the outside of the back cover of Volume III. If the worm travels in a straight line, how far does it travel?

Answer: The worm actually only travels one inch. The way the books are lined up, volume one is on the left so it's front cover is to the right (next to vol. 2's back cover) and volume 3's back cover is on the left (next to the front cover of vol. 2's) so the cute little worm only goes an inch.

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The Boulders

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The mean weight of twelve boulders is twenty-five pounds. Adding another boulder increases the mean weight to twenty-nine pounds. What is the weight of the thirteenth boulder?

Answer: 77lbs. The total weight of the original twelve boulders is 12 x 25 = 300 pounds. After the new boulder is added, the total weight is 13 x 29 = 377 pounds.

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Probability and the Number 48

One of the factors of 48 is chosen at random. What is the probability that the chosen factor is not a multiple of 4?

Answer: The only factors of 48 that are not mutliples of 4 are 1, 2, 3, 6. There are a total of 10 factors. So, 4/10 is the probability reduces down to 2/5.

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The Ski Lift

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James is sitting on the ski lift, which is a continuous loop with chairs that are numbered consecutively. Exactly halfway up the ski slope, he notices that chair number 9 passes him on the way down. He is sitting on chair 81. How many chairs are on the ski lift?

Answer: 144. Since James is at the halfway point on the lift, an equal number of chairs are above and below him. 71 chairs come between chairs 9 and 81. (Sketch a smaller eight-chair lift to illustrate this concept.) Chairs 9 and 81, plus the 71 above and the 71 below, total 144 chairs.

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The Grid

Arrange the numbers 1 through 16 in a 4 x 4 grid so that consecutive numbers are not touching.

Answer: One possible solution.

1 14 5 7
16 8 10 12
11 13 15 4
3 6 2 9

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Page by: Mathman (Bruce A. Titen) 1998

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