Around the Dartboard
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|Ivars Peterson (MathLand)|
|The numbers on a standard dartboard have the following order, going clockwise starting at the top: 20, 1, 18, 4, 13, 6, 10, 15, 2, 17, 3, 19, 7, 16, 8, 11, 14, 9, 15, and 5. Why this particular order? A possible criterion for designing a dartboard is to penalize poor shots as much as possible. That can be done, for example, by maximizing the sum of the absolute value of the difference between adjacent numbers. The larger this sum, the more a poor shot is penalized. To achieve this maximum, the numbers 11 to 20 should interlace 1 to 10. In this case, the differences between adjacent numbers total 200.|
|Levels:||High School (9-12), College|
|Resource Types:||Problems/Puzzles, Articles|
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