Luc, Mechteld and Sjoerd are hungry, so they each give Mitch €10, together €30, and send him to the Spar to get some food. The food costed €25 (it was a lot of food!) but Mitch realises the remaining €5 can't be split evenly over Luc, Mechteld and Sjoerd, so he decides to return €1 to each of them and to pocket the remaining €2. Now Luc, Mechteld and Sjoerd each paid €9, together €27, and Mitch got €2, making the total €29 and not €30! Where did the remaining euro go?
Solution of the previous puzzle: We distinguish between 4 cases: the first and the second person can both be either Estimator or IntAct. Suppose they are both Estimator. Then from the first person's answer we deduce the third person is also Estimator, so he will truthfully say the first and second person are both of Estimator. Second case: suppose they are both IntAct. Then the first person lied, meaning the third person is not of IntAct but of Estimator, so he will again truthfully say the first two persons are of the same committee. Third case: suppose the first person is Estimator and the second IntAct, then the third person will also be IntAct and will not tell the truth. Hence, he will say the first two people are of the same committee. Fourth case: suppose the first person is IntAct and the second Estimator, meaning the third person is IntAct and will lie and say the first two persons are of the same committee!
Q.e.d.