MathDB

There are

100

people in a room. Some are wise and some are optimists.
\bullet~ A wise person can look at someone and know if they are wise or if they are an optimist. \bullet~ An optimist thinks everyone is wise (including themselves).
Everyone in the room writes down what they think is the number of wise people in the room. What is the smallest possible value for the average?

\mathrm a. ~ 10\qquad \mathrm b.~25\qquad \mathrm c. ~50 \qquad \mathrm d. ~75 \qquad \mathrm e. ~100

Problem Statement