Probability Level 2

Alice and Bob encountered a stall selling chocolate milk--their favorite! However, they only have enough money to buy one drink and share. In front of them are 10 cups of milk arranged in a row, and each of them is assigned a value--the higher the value, the higher the temperature:

1,3,3,7,9,1,8,4,5,2.1, \, 3, \, 3, \, 7,\, 9, \, 1,\, 8, \, 4, \, 5,\, 2.

The problem arises when Alice wants the milk to be as warm as possible, but Bob wants it to be as cold as possible. So, they will play a game to decide which cup of milk they will buy. They will play alternately, and Alice will go first. The process for each player is as follows:

  1. Remove 3 consecutive cups from the table.
  2. Merge the rest of the cups without changing the order.

The game ends when there is only 1 cup left, and they will buy it. Assuming that both Alice and Bob play optimally, what is the temperature of the milk they will buy?


Problem Loading...

Note Loading...

Set Loading...