(1) A wine merchant dies, leaving his three sons seven barrels full of wine, seven barrels half-full of wine, and seven empty barrels. He specifies that each son shall receive exactly the same number of full, half-full, and empty barrels. Can his wish be carried out?
(2) A sheik died, leaving seventeen camels. His will specified that they be divided among his three sons as follow: ½ to the eldest, 1/3 to the second, and 1/9 to the youngest son. When the three sons were puzzling over how this could be done, a wise man happened to ride by on a camel. How did the wise man solve the problem?
(3) A king wants to pass his throne to one of his two sons. He decrees that a horse race shall be held and the son who owns the slower horse shall become king. The sons, each fearing that the other will cheat by having his horse go less fast than it is capable of, ask a wise man’s advice. With some words the wise man insures that the race will be fair. What does he say?
(4) On an island there are two races: Whites and Reds. Whites always tell the truth and Reds always lie. You are introduced to three natives named Tom, Dick, and Harry. You ask each of them one question. “Tom, is Dick a White?” “Yes.” “Dick, do Tom and Harry belong to the same race?” “No.” “Harry, tell me about Dick.” “He is a White.” Can you determine the race to which each belong?
(5) Whites always tell the truth and Reds always lie. You are rowing toward shore, on which you see three men. You shout to them, “Are you White or Red?” The first man answers, but his words are blown in the wind. The second cries, “He says he’s White. Yes, he’s White, and so am I.” The third cries, “He’s Red, but I am White.” What is the race of each of the three men?
(6) On an island dwelt three races: Whites, Reds, and Pinks. Whites always tell the truth. Reds invariably lie. Pinks alternately lie and tell the truth, but we never know whether a Pink’s first answer will be true or not. The only certainty is that if his first answer is truthful, his second answer will be a lie, and vice versa. A smart man met three men named John, Bob, and Ted. One of the three was a White, one a Red, and one a Pink, but he didn’t know to which race they each belonged. The smart man only said to John. “John, what’s your race?” “I’m a Pink.” “And Bob?” “He’s a White.” “So Ted is a Red.” “Obviously.” To what race did each belong?
(7) A king locks a captive in a room with two servants, one who always tells the truth and one who always lies. The room has two doors: the door to freedom and the door to slavery. The captive must decide his fate by asking one question to only one of the servants. He doesn’t know which is the liar. How is the captive sure to gain his freedom?
(8) A farmer with a chicken, a fox and a bag of grain, come to a river. The boat is only large enough to carry he and one of the others. Since the fox can eat the chicken and the chicken can eat the grain, how can they all be taken safely across without any unwanted lunch?
(9) Three men, traveling with their wives, come to a river and find one boat that can hold only two people at a time. Since all the husbands are extremely jealous, no woman can be left with a man unless her husband is present. How do they cross the river?
(10) Three scientists and three cannibals come to a river. The boat available can carry only two people at a time. If there are more cannibals than scientists, the latter become dinner. How can they all get across?
A N S W E R S
(to keep you from staying awake all night)
(1) Pour one of the full barrel into the empty one to make two more half-full. Now there are six full, nine half-full and six empty barrels. All can be divided by three.
(2) He added his own camel, making the division easy: ½ x 18 = 9; 1/3 x 18 = 6; 1/9 x 18 = 2. Since the total is 17, the wise man took back his own camel.
(3) “Switch horses.”
(4) Tom and Harry must be of the same race, because answered the same question identically. So Dick was lying and must be a Red. Since Tom and Harry said Dick was a White, they also answered untruthfully. Therefore all three are Reds.
(5) Either the first man White or Red, the words blown away by the wind were “I’m White.” So the second man told the truth. Since the first two men are both White, the third man obviously is Red.
(6) John is not a White, for if he is, he would say so. He is not a Pink, for if he is, his first answer is right and hence his third answer must also be right. If this is the case, his second answer is also right, which is impossible. So John is a Red: all his answers are untruthful. Bob is a Pink and Ted is a White.
(7) The captive asks either servant, “If I ask you to show me the door to freedom, which door will you point to?” Either servant will point to the door to freedom.
(8) Take the chicken across, then the grain. Bring the chicken back and take the fox across. Next return for the chicken.
(9) A and wife cross, A returns. B’s and C’s wives cross, A’s returns. B and C cross, B and wife return. A and B cross, C’s wife returns. A’s and B’s wives cross, C returns. C and wife cross.
(10) Two cannibals cross, one returns. Two cannibals cross, one returns. Two scientists cross, one cannibal and one scientist return. Two scientists cross, one cannibal returns. Two cannibals cross, one returns. Two cannibals cross.***