2005 iTest Problems/Problem 15
Problem
Kathryn has a crush on Joe. Dressed as Catwoman, she attends the same school Halloween party as Joe, hoping he will be there. If Joe gets beat up, Kathryn will be able to help Joe, and will be able to tell him how much she likes him. Otherwise, Kathryn will need to get her hipster friend, Max, who is DJing the event, to play Joe’s favorite song, “Pieces of Me” by Ashlee Simpson, to get him out on the dance floor, where she’ll also be able to tell him how much she likes him. Since playing the song would be in flagrant violation of Max’s musical integrity as a DJ, Kathryn will have to bribe him to play the song. For every 
she gives Max, the probability of him playing the song goes up 
(from 
to for the first , from to 
for the next , all the way up to 
if she gives him 
). Max only accepts money in increments of . How much money should Kathryn give to Max to give herself at least a 
chance of securing enough time to tell Joe how much she likes him?
Solution 1
This is related to Problem 13, where we find that Joe has (spoiler) a 17% chance to get beat up. The equation 
represents the current problem where 
is the number of times Kathryn must pay Max: 
. And since must be a whole number for the solution to make sense, it must be rounded up, 
See Also
| 2005 iTest (Problems, Answer Key) | ||
| Preceded by: Problem 14 |
Followed by: Problem 16 | |
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