Question

2. Three players (Adam, Bob and Chad) are sharing a cake. Suppose that the cake is divided into three slices (s1, s2, s3). The following table shows the value of s1, and of s2 to teach of the players. The values of s3 are missing. (The percentage represent the value of the slice as a percent of the value of the entire cake)

s1 s2
Adam 30% 50%
Bob 32% 36%
Chad 30% 35%

a. Which of the three slices are fair shares to Adam?
b. Which of the three slices are fair shares to Bob?
c. Which of the three slices are fair shares to Chad?

Answer 1

You need to define what's "fair" here. None of the choices provides equal amounts to all three. Is any of them fair to anyone?

Maybe fairness depends on weight, or hunger, or social standing. This question is meaningless without an explanation of what's fair.

If by "fair" you mean which provides at least 1/3 of the cake to a person, then
#1 is "fair" only to whoever gets s2.