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Bowling averages in your spare time.

Bowling averages in your spare time

If you think bowling a perfect score of 300 is hard, try figuringout how many different ways a bowler can roll, say, a 147, or for that matter, any other score. Starting at zero, the first case is easy to compute. A hopelessly incompetent bowler can score a zero in only one way--by missing all 10 pins with both balls in each of 10 tries. There are 20 ways to record a one: You can knock over one pin with your first or second ball in any one of the 10 frames. But for larger scores, the calculations get more complicated, and the number of possibilities escalates rapidly.

Now the numbers are known, courtesy of mathematiciansCurtis N. Cooper and Robert E. Kennedy of Central Missouri State University in Warrensburg. Both bowl regularly, and they decided to spend some spare time working out the appropriate figures. Because of the complex scoring system used in 10-pin bowling, says Kennedy, "it turned out to be a tricky mathematical problem."

Out of about 5.7 billion billion possible games, the strikingresults show that there are more ways to bowl a 77 than any other score. That score comes up 172,542,309,343,731,946 times. In contrast, there are only 51,701,385,089,887 ways to bowl a 147, merely 1,526,313,637 ways to reach 200, and of course, only one way to score a 300. When all possible scores are added together and then divided by the total number of possible games, the mean score comes to an "awful" 80.

"This won't help you bowl any better," says Cooper, "But itmay make you feel better about your own score."
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Title Annotation:recreational mathematics
Author:Peterson, Ivars
Publication:Science News
Date:Aug 16, 1986
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