Home > Problem of the Week > Archive List > Detail

 << Prev 4/17/2011 Next >>

## Play With These Old "Logic" Classics

Many problems are repeated to the point that they become classics. Below are three such "logic" classics, possibly in new clothes.

[#1] Three travelers share their meals. Man A contributes five dishes, man B three dishes, and man C pays \$8. Assuming the eight dishes are all worth the same amount of money, how should the \$8 be divided between the man A and man B?

[#2] The King wants to oust his prime minister. He summons him to the throne room, holds out two slips of paper and says: "On one of these I have written LEAVE and on the other STAY. The paper you draw will decide your fate." The prime minister is certain that LEAVE is written on both slips, how can he keep his position?

[#3] The sultan locks a female captive in a room with two servants, one who always tells the truth and one who always lies. The room has two doors--a door to freedom and a door to slavery. The captive will decide her fate by choosing an exit door. Now, the captive can ask one question of one of the servants, but does not know which is the liar. How can she be certain to pick the right door to freedom?

Source: J. Baillif's "Let's Cere-brate," Reader's Digest, 1982, p. 27

Hint: Stop...Think...Use "clever" logic in your response.

Solution Commentary: Author Baillif offered these responses as solutions...do you agree with him?

[#1] Man C's contribution of \$8 implies the entire meal cost \$24, or \$3 per dish. Thus, man A brought \$15 worth of dishes and man B brought \$9 worth. Thus, split the \$8 so man A gets \$7 and man B gets \$1.

[#2] The prime minister grabs one slip, wads it up, and eats it....without anyone looking at it. Since the King's remaining slip says LEAVE, the king is forced to agree that the other "swallowed" slip must have said STAY.

[#3] The captive asks either servant: "If I ask the other servant to point out the door to freedom, which one will he point to?" In response, both servants would point to the door to slavery; she should choose the other door.