Consider the guessing game where people are choosing numbers between 0 and 100. Choices must be in whole numbers. The aim is to come as close as possible to (2/3) of the average number chosen in the group. We will define "Level 0" thinking to imply that everyone chooses 100, in which case the average is 100 and 2/3 of the average is 67. Suppose you believe that two-thirds of the group will apply Level 1 thinking while the other one-third applies Level 2 of thinking. What should you choose? Choose the whole number that you believe would be closest to the answer.
A) 40.
B) 13.
C) 25.
D) 19.

Question

Quizplus · Accepted Answer

Level 1 thinking implies choosing 2/3 of the average, which is 67. Level 2 thinking implies choosing 2/3 of the average of the Level 1 choices, which is 2/3 of 67, or 45. So, the average of the Level 1 and Level 2 choices is (2/3) * 67 + (1/3) * 45 = 56. Therefore, the best choice is 2/3 of 56, which is 37.33. Since we must choose a whole number, the closest choice is 40.

Consider the Guessing Game Where People Are Choosing Numbers Between