The Great Grasshopper Race

Aug 24, 2002

RAY: Two grasshoppers are hanging around, and each is boasting that he is faster than the other. To settle the argument, they decide to have a race.

The larger of the grasshoppers, Throckmorton -- or Throckie, as he's known -- can jump 10 inches at a single bound. The other grasshopper, Rocky, can jump only six inches at a shot. So the larger grasshopper says, "We're going to set up a racecourse that's 24 feet long: 12 feet out and 12 feet back."

They're each at the starting point. Vinnie Goombatz-Hopper shoots the gun, and they take off.

Now, even though Throckie, the bigger guy, can jump 10 inches at a shot, the little guy, Rocky, jumps more often. So when they get to the five-foot mark -- which is 60 inches -- the big guy has jumped six times and the little guy has jumped 10 times, but they're dead even...neck and neck...antennae to antennae.

The question is: Which one wins the race, and why?

Answer: 

TOM: Yeah. This was immediately apparent. This was a very easy puzzle.

RAY: Because the course is 12 feet, or 144 inches, the little guy, jumping six inches at a shot. Admittedly they're even at five feet, and they're even at 10 feet too. But when they get to 12 feet, trouble breaks out because the little guy happens to land right on the turnaround point.

TOM: Exactly.

RAY: With 24 jumps.

TOM: Yeah.

RAY: After 14 jumps Throcky is at 140 inches, and his next jump brings him to ... and he has to make a 10-inch jump.

TOM: Yeah, he can't make little jumps.

RAY: So the little guy, as you suspected, wins the race.

TOM: Sure.

RAY: Do we have a winner? Good guys always finish last, hunh?

TOM: Yeah, we got a winner. The winner is Sue Spooner from Estes Park, Colorado.


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