A state tennis tournament has 162 players in singles competition. Players play until they lose a match and are thus eliminated. If, at any stage of the tournament, there is an odd number of players remaining, one player is given a “bye” and sits out a round before playing again. How many matches must be played to determine the tournament champion?

In one final, desperate attempt to get him to make his bed, Rick’s father offered to pay him 15 cents every day that he made his bed but fine him 12 cents every day that he did not, beginning on January 1, 2009. As of December 31, Rick had collected $53.40. On how many days had he failed to make his bed?

Ferman Fink was the host at a Valentine’s Day party last year. In answer to a question from a guest, Ms. Phoebe Beebe, Ferman said, “I have three daughters and I will tell you how old they are. The product of their ages is 72. The sum of their ages is my house number.” Phoebe thought for a few moments. Then she went out and looked at the house number. She came back in and told Ferman that he had not given her enough information to solve the problem. Ferman then said, “Okay, my oldest daughter likes vanilla yogurt.” Phoebe immediately told him the ages of the three girls. Can you do the same? (All ages are whole numbers.)

Charlie and LaQuanda plan to meet at the railroad station to take the train that leaves at 8:00. Charlie thinks his watch is 25 minutes fast, but it is actually 10 minutes slow. LaQuanda thinks her watch is 10 minutes slow, but in fact it is 5 minutes fast. Each one looks only at his/her own watch. The two plan to meet each other at the station at 7:55. What happens?

Tony goes into Dave’s Army-Navy store and buys a hat for $14. He gives Dave a $20 bill. Dave doesn’t have any change, so he takes the $20 bill across the street to Laura, the clerk in Watson’s Hardware store. Laura trades Dave’s $20 bill for twenty $1 bills. Dave comes back and gives Tony $6 in change. Tony takes the hat and the $6 change and leaves town forever. Half an hour later Laura comes over to Dave�s store, just furious. She has discovered that the $20 bill he gave her is counterfeit. Dave, of course, makes it good, giving Laura a genuine $20 bill he has in the till from an earlier sale. Question: Now that it is all over, who came out behind? And by how much?

Sherman is chasing his pet frog Cyrus. Sherman takes 2 steps while Cyrus makes 3 jumps, but Sherman’s steps are twice as long as the frog’s jumps. The frog had made 10 jumps before Sherman noticed and started chasing him. How many more jumps will Cyrus make before Sherman catches him?

In the 10 cells shown here, you are to inscribe a 10-digit number such that the digit in the first cell tells how many zeros are in the entire 10-digit number, the digit in the cell marked “1” tells how many 1’s are in the number, and so on. Thus, if the “4” cell has a 2 in it, then there are two 4’s somewhere in the 10-digit number.