MathDB

Four friends, Anna, Bob, Celia, and David, exchanged some money. For any two of these friends, exactly one gave money to the other. For example, Celia could have given some money to David but then David would not have given money to Celia. In the end, each person broke even (meaning that no one made or lost any money).
(a) Is it possible that the amounts of money given were

10

20

30

40

50

60

? (b) Is it possible that the amounts of money given were

20

30

40

50

60

70

?
For each part, if your answer is yes, show that the situation is possible by describing who could have given what amounts to whom. If your answer is no, prove that the situation is not possible.

Problem Statement