The twins Polly Dent and Pepso Dent decide to play a betting game using their weekly allowance of $30. Each twin antes up $20.
Polly picks a random whole number from 1 to 10.
Then, Pepso must select a second (and different) whole number from 1 to 10.
Their trusty TI is used to print out a random whole number from 1-10.
The winner of the $40 "pot" is the person whose number is the closest to the TI's random number. (Note: On a tie, they split the pot for that week).
Task 1: Devise a strategy for Pepso so that he will win more times than his twin sister Polly.
Task 2: Could you devise a winning strategy for Pepso for every whole number range 1-N? Explain.
Hint: Devise a plan...test it...refine it....test it...etc.
Solution Commentary: Would it help to reduce the situation to a simpler situation, such as a number range 1-3, 1-4, 1-5, etc.?
Would it help to work the problem backwards? That is, suppose Pepso picked the number x and then look at which cases it would be a winning number (for various values of both Polly's number and the TI's number).