A Little Bit of Everything

Hint: Sometimes it helps to read the questions aloud.

1. What is the next row of digits?

1
1 1
2 1
1 2 1 1
1 1 1 2 2 1
3 1 2 2 1 1
1 3 1 1 2 2 2 1
1 1 1 3 2 1 3 2 1 1
? ? ? ? ? ? ? ? ? ?

2. Where would you place the 9 and the 10 to keep the sequence going and why? 1. A wire of 1/100 of a inch in diameter is tightly wound into a ball with a diameter of 24 inches. It is assumed that the wire is so solidly packed that there are no air gaps in the ball. Can you determine the length of the wire?
2. A book costs \$1 plus half its price. How much does it cost?
3. A prisoner was sentenced to be executed but was given a chance at freedom if he drew a silver ball from one of two identical urns. He was allowed to distribute 50 silver and 50 gold balls between the two urns any way he liked. The urns were then going to be shuffled aroud out of his sight and he was to pick one urn and draw one ball at random from it.
How did the prisoner maximize his chances of success? If he put equal numbers of gold and silver balls into one urn the the other urn would also have equal numbers of gold and silver balls and then the probability of his drawing a silver ball would have been 1 in 2. Can you determine haw he was able to improve his chances?
4. What is the next word in the sequence: aid, nature, world, estate, column, sense…?
5. Prove with a simple equation that the product of four consecutive integers can not be a perfect square.
6. Is it possible to move a knight (horse) on a chessboard from the lower left corner (a1) to the upper right corner (h8), and visit every square on the board once?
7. Transposing the two digits of A’s age gives you B’s age. The difference between the their ages gives you twice C’s age and B is ten times as old as C. What are the three ages?
8. Complete the square:

 1 1 1 1 1 3 5 7 1 5 13 25 1 7 25 ??

1. If eight men can dig sixteen holes in thirty-two days, how long will it take four men to dig eight holes of the same size?
2. How many squares are on a chessboard?