Aaron, Brian, and Dwayne went on a hike, carrying a bag of apples. They stopped for a nap. Aaron woke up, ate 1/3 of the apples, and went back to sleep. Later Brian woke up, ate 1/3 of the remaining apples, and went back to sleep. Finally Dwayne woke up and ate 1/3 of the remaining apples. There were now 8 apples left in the sack. How many apples had been there originally?
Set 03
Prom Band
It is time to hire the band for the prom. Band A will play for $2500 plus 50% of the money taken in from ticket sales. Band B will play for the flat fee of $5500. You expect 300 couples to attend. What is the most you can charge per couple so that Band A is cheaper than Band B?
Newspaper Tearing & Stacking
A single sheet of newspaper is .01 cm thick. Tear it in half and stack the two halves together. Tear the two halves in half and stack the 4 pieces together. Keep it up. How tall is the stack after 25 tears? How many tears do you need to get a stack that is 1 meter high?
Consecutive Integers, Sum of 100
Find all sets of consecutive positive integers whose sum is 100. How many such sets are there?
False Coins 1
You are applying for a job as inspector at the U.S. Mint. You have been handed 8 gold coins and are told that one of them is counterfeit; it is slightly lighter than each of the other seven. You are given a two-pan balance scale, and you are told that you may make two weighings on that scale. How can you identify the counterfeit coin? (Your prospective employers are fussy about the scale; if you put some coins on for the first weighing, and then change the coins in any way, that counts right there as your second weighing.)
Ant, Bat, Cat
I have three stuffed animals: an ant, a bat, and a cat. One is red, one is white, and one is blue. Exactly one of these statements is true:
- The ant is red.
- The bat is not red.
- The cat is not blue.
Tell the color of each animal.
Messrs. Blue, White, Gray
Mr. Blue, Mr. White, and Mr. Gray are wearing shirts and ties that are blue, white, or gray. Each man’s tie contrasts in color with his shirt, and neither the shirt nor tie matches the man’s name. If Mr. Blue’s tie is the same color as Mr. Gray’s shirt, what is the color of Mr. White’s shirt?
Missing Dollar
Three Hollywood talent scouts were in town to watch the spring play production at the high school. After the show they went to the Parma Gianna Pizza Palace and ordered three $10 pizzas for a total of $30. Ten minutes later, Mike the cashier approached them and said there was a special on pizzas that day — buy two, get one half price — so they only owed $25. He gave them back the extra $5 they had paid. Not knowing how to split the $5 three ways evenly, the scouts gave Mike $2 as a reward for his honesty and kept $1 apiece for themselves. This means that each man paid $9 for his pizza, or $27 for the three pizzas. Mike got $2, making $29. What happened to the other dollar?
Blue Cube, 27 Little Cubes
A three-inch blue cube is cut up into 27 little cubes. The inside of the cube is white. How many of the 27 little cubes have one blue face? Two? Three? More than three?
This Man’s Father
Quarteen Baxton shows a photograph of a man to a friend and says, “Brothers and sisters have I none, but this man’s father is my father’s son.” What relation is Baxton to the man in the photo?