This summer, there was increased interest in the
Powerball lottery when the jackpot offered $295
million. A group of machinists calling themselves
"The Lucky 13" won the jackpot and took a cash
payout of $161.5 million, with each receiving
$8,944,447 after taxes. Their winning numbers
were 8-39-43-45-49 and powerball 13.
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.
Now five white balls are chosen from those numbered
from 1 to 49, 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 300,000. 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 50 and the maximum number for
the Powerball is 50).
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:
49 C 5 * 42 = 80,089,128 After examining all combinations of balls up to 50, only one solution gives us odds of one in 300,000:
Use white balls numbered from 1 to 18, and choose the Powerball from balls numbered 1 to 35.
18 C 5 * 35 = 299,880 The next closest values are:
19 White balls, 26 for powerball: 19 C 5 * 26 = 302,328
24 White balls, 7 for powerball: 24 C 5 * 7 = 297,528
23 White balls, 9 for powerball: 23 C 5 * 9 = 302,841
Correctly solved by:
| 1. John McKay | Charlottesville, VA |
| 2. Ryan Dutton | Winchester, VA |
| 3. John Beavers | Winchester, VA |