Answer to January 27, 2003 Problem |
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Powerball Problem This winter, there was increased interest in the Powerball lottery when the jackpot offered $315 million, which was won by a man in Hurricane, West Virginia.Powerball was first introduced in 1987 and the odds of winning were 1 in 55 million. Five white balls were picked from balls numbered from 1 to 45 and one powerball was picked from another set of balls numbered from 1 to 45. In November 1997, officials raised the odds of winning to one in 80 million, thus making likely jackpots of at least 100 million dollars twice a year. Five white balls were chosen from those numbered from 1 to 49, and the powerball was chosen from another set numbered from 1 to 42. Currently, the odds of winning Powerball are 1 in 120,526,770. Five white balls are chosen from those numbered from 1 to 53, and the powerball is chosen from another set numbered from 1 to 42. Suppose you want to lower the odds of winning Powerball to one in 250,000. What should the range of the white balls be and what should the range of the powerball be? (The maximum number of white balls that you may use is 55 and the maximum number for the Powerball is 55). |
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Solution to Problem:
The odds are calculated by computing the
combination of the white balls taken 5 at
a time, and then multiplying by the number
of balls from which the Powerball is chosen.
For example, the odds for the original Powerball
is figured in the following manner: 45 C 5 * 45 = 54,979,155 Likewise, the current Powerball odds: 53 C 5 * 42 = 120,526,770 After examining all combinations of balls up to 55, there are none that give us odds of exactly one in 250,000. The closest would be: Use white balls numbered from 1 to 18, and choose the Powerball from balls numbered 1 to 29. 18 C 5 * 29 = 248,472 The next closest values are: 20 White balls, 16 for powerball: 20 C 5 * 16 = 248,064 17 White balls, 40 for powerball: 17 C 5 * 40 = 247,520 17 White balls, 41 for powerball: 17 C 5 * 41 = 253,708 |
| 1. Richard Johnson | La Jolla, California |
| 2. Rick Jones | Kennett Square, Pennsylvania |
| 3. William Funk | San Antonio, Texas |
| 4. Gadi Manor | Herzeliya, Israel |
| 5. John Funk | Ventura, California |
| 6. Chris White | Chicago, Illinois |
| 7. Joe Jenkins | Winchester, Virginia |
| 8. Jeff Gaither | Winchester, Virginia |
| 9. Walt Arrison | Philadelphia, Pennsylvania |
| 10. Tom Dressen | --------- |
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Honorable Mention: David and Judy Dixon from Bennettsville, SC, and Elizabeth Harp from Columbus, GA sent in solutions that were very close. |