1. Which one of the following doesn’t belong: pitying, favor, unkindness, murder, exaltation?

2. A climber leaves camp at midnight for the top of the mountain and arrives there at noon. He immediately turns around and climbs back down by the same route to arrive at camp at midnight, exactly 24 hours after he left it. Is it [...]

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Tom
Walking home one day to your little pied-a-terre outside Pamplona, you take a short cut along the train tracks. The tracks cross a narrow bridge over a deep gorge. At the point you are 3/8 of the way across the bridge, you hear the train whistle somewhere behind you. You charge across the bridge, and [...]

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Tom
In each of six boxes B1, B2, B3, B4, B5, B6 there is initially one coin. There are two types of operation allowed:

Type 1: Choose a nonempty box Bj with 1 ≤ j ≤ 5. Remove one coin from Bj and add two coins to Bj+1.

Type 2: Choose a nonempty box Bk with 1 ≤ k ≤ 4. Remove one coin from [...]

As your basic, average, everyday, ho-hum, run-of-the-mill super spy, you sometimes need to exchange information with other agents. Your preferred method of communicating is to leave messages in a public strongbox. These strongboxes are made from Unobtanium and are indestructible, and immovable. If you want security on these, you need to provide your own padlock [...]

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Tom
In preparation for an Easter Egg Hunt, Euclid’s mother purchases a dozen eggs. She boils half the eggs, marks each of them with a small “X”, and puts them back in their carton with the rest. Presumably, the remaining eggs will be used for some other less festive purpose like breakfast.

The smallest child of the [...]

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Tom
In a strange world there are n airports arranaged around a giant circle, with exactly one airplane at each airport initially. Every day, exactly two of the airplanes fly, each going to one of its adjacent airports. Can the airplanes ever gather at one airport?

a) Prove that the geometric mean of two positive numbers is equal to the geometric mean of their arithmetic and harmonic means.

b) Prove that the harmonic mean of two positive numbers a and b does not exceed the geometric mean, and that the equality holds only if a=b.

c) Prove that the arithmetic mean of three positive [...]

Prove, given any three positive numbers a, b, and c, the following inequality holds: (a+b)(b+c)(c+a)≥8abc.

Show that the equality holds only for a=b=c.

A butcher has an inaccurate balance scale (its beams are of unequal length). Knowing that it is inaccurate, and being an honest merchant, he weighs his meat as follows. He takes half of it, and places it on one pan, and he places the weights on the other pan; then he weighs the other half [...]

Eketahuna and Slavy were sitting at the bar celebrating their new three year contracts.Eketahuna said that he starts at $50,000 a year and will get a $10,000 raise at the beginning of each year.Slavy starts at $25,000 for the first six months,and gets a $2,500 raise every six months after that.

Who got the better deal.

also,why [...]