Five out of Six ain't bad....

1)You have two coins in your pocket that add up to 26 cents. One of them is not a quarter. What are the coins? (easy)

Solution: A quarter and a penny. The one that is NOT the quarter is the penny. A play on words.

2) A cylindrical hole 6 inches long is drilled straight through the center of a solid sphere. What is the volume remaining in the sphere? (hard)

Solution: 36 Pi cubic inches.

If you want to avoid the calculations in Solution 1, simply take a look directly at Solution 2 below it.

Solution 1
Let R be the radius of the sphere. As the illustration indicates, the radius of the cylindrical hole will then be the square root of R² - 9, and the altitude of the spherical caps at each end of the cylinder will be R - 3. To determine the residue after the cylinder and caps have been removed, we add the volume of the cylinder, 6π(R² - 9), to twice the volume of the spherical cap, and subtract the total from the volume of the sphere, 4πR³/3. The volume of the cap is obtained by the following formula, in which A stands for its altitude and r for its radius: πA(3r² + A²)/6.

When this computation is made, all terms obligingly cancel out except 36π - the volume of the residue in cubic inches. In other words, the residue is constant regardless of the hole's diameter or the size of the sphere!

Solution 2
John W. Campbell, Jr., editor of Astounding Science Fiction, was one of several readers who solved the sphere problem quickly by reasoning adroitly as follows: The problem would not be given unless it has a unique solution. If it has a unique solution, the volume must be a constant which would hold even when the hole is reduced to zero radius. Therefore the residue must equal the volume of a sphere with a diameter of six inches, namely 36π.

3) Three rabbits are crossing the road, a busy road. A father rabbit, a mother rabbit, and a baby rabbit. Suddenly the strong father rabbit sees a chance, takes up baby in his arm, and drags the mother rabbit by the other hand across the road. They arrive there without injury. The baby rabbit then says "Thank you daddy, for getting all two of us across the road safely" Please explain. (medium)

Solution: The baby rabbit was so young it could not count beyond two.

4) You have three cards, (two aces and a queen), all face down. You are asked to find the queen, and you are asked to pick one card only. Then , the magician looks at them all, and promptly turns face up , an ace. What is the probability that your card is the queen? (hard)

Solution: 1 in 3. The probability that your card is the Queen is 1 in 3 because you chose it before the magician turned over any cards. In fact, at any time after the choice, he can always turn over an ace. Try it with the whole pack – it is easier to see then. The dealer then turns over 50 cards that are NOT your chosen one. In this case, the probability remains 1 in 52, As the magician can ALWAYS turn face up 50 cards that are NOT yours!!! Poor Jeffrey!

5) A snail falls into a well which is 20 meters deep. He starts to climb up immediately, and in the daytime, he goes three meters up, but at night falls two meters back again. Assuming he starts the ascent at dawn on the first day, how many days is it before he emerges? (easy)

Solution: 18 days. After 17 days and nights, he is 3 meters below the rim. On the morning of the 18th day, he simply climbs up his lasy daily 3 meters to EMERGE triumphant.