MathDB

300

couples (one man, one woman) are invited to a party. Everyone at the party either always tells the truth or always lies. Exactly

2/3

of the men say their partner always tells the truth and the remaining

1/3

say their partner always lies. Exactly

2/3

of the women say their partner is the same type as themselves and the remaining

1/3

say their partner is different. Find

a

, the maximum possible number of people who tell the truth, and

b

, the minimum possible number of people who tell the truth. Express your answer as

(a,b)

Problem Statement