Vinnie Goombatz and the 247 Arm Wrestlers
RAY: This is stolen somewhat from an e-mail I got a long time ago. Here we go. Our erstwhile companion and chief mechanic, Vinnie Goombatz, being renowned for his prowess in arm wrestling, is asked to set up a tournament at the local watering hole where he goes and gets stewed every night. It's to be a single elimination tournament, i.e., once you lose, you're out. No ties allowed. This is arm wrestling; you can't have a tie in arm wrestling, right?
RAY: To his horror, 247 people have signed up for this tournament, and the barkeeper wants to know how many bouts have to be fought. Figuring a bout takes about five minutes, he wants to know at what time he should start the event so that it will conclude before closing time.
So Vinnie is in a tizzy now, because he's thinking about, Oh, I gotta set up a branching tree, count all the branches, and since he can't count much beyond 14, he's in a tizzy.
Fortunately, there's a little guy sitting next to Vinnie at the bar, and the guy says, "I know the answer." Vinnie says, "What are you, some kind of genius or sump'm?" The guy says, "No, but there is a simple reasoning process which will allow you to instantly know how many bouts have to be fought."
The question is: If there are 247 people that signed up, how many bouts will there have to be in order to determine one winner?
TOM: With a single-round elimination.
RAY: And show your work. And, by the way when the bout starts, both hands of the clock are 180 degrees apart.
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[ Car Talk Puzzler ]