Recreational Mathematics

Logic Puzzles

These are logic puzzles. The most famous being the Liar's Paradox. Consider the statement: "I'm a liar." Is this made by a truthteller or a liar? If it's a truthteller, then the statement contradicts his status as a truthteller; if it's a liar, then it's a true statement, which again is contradictory to his status as a liar. Hence, no statements in mathematical puzzles can contain such a type of statement.

(1) A stranger comes to a Y-junction and doesn't know which way to go. There are 2 men at the junction, one of whom is a truthteller, which the other is a liar. The stranger doesn't which is which. He may ask only one of them one question. What should he ask and to who?

(2) Ellen was in a card game with 3 of his friends. Given these situation, can you deduce who's who?

a) Bill and Clark had better scores than the engineer.

b) Bill dealt the cards in the order: Clark, Mr Irving, the bartender, himself.

c) When it was Clark's turn to deal, he followed this order: the pianist, Mr Irving, Dilbert, himself.

d) Mr Flint went off before Dilbert

e) the engineer had a better score than Mr Halls.

f) Mr Gerard went off before the pianist.

(3) John met 3 persons, A, B and C. John asked A whether he's a truthteller or a liar. A mumbled something. John then asked B:" What did he say?" B said:" A said he's a truthteller." C then said:" B is lying." Was C a truthteller or a liar?

(4) There are 3 persons: a truthteller, a liar and an alternator (alternates between truth and lie). After a race, they made the following statements:

A: I came in second. B came in last.

B: A came in last. C won.

C: I came in last, A won.

Who's in which position?

(5) In a card game, there are 3 persons, A, B and C. Amongst them there are 3 nationalities, Singaporean, Malaysian and Indonesian. They sit in a circle and each pass 1 card to the one on the right. B passed to the Singaporean, A passed to the person who passed the card to the Indonesian. Who's who?

Next Page: Probability Puzzles.

Answers:

(1) He can ask either of the men the following question while pointing at one of the directions at the junction: "If I were to ask you if this is the way I should go, would you say yes?"

(2) Bill Flint is the pianist, Ellen Irving is the engineer, Dilbert Halls is the bartender, Clark Gerard is the administrator.

(3) Regardless of whether A is a liar or a truthteller, he would say:" I'm a truthteller". So B is telling the truth and C is lying.

(4) C won, A second, B last.

(5) A is the Singaporean, B the Indonesian and C the Malaysian.