Logic Building Problems

LOGIC BUILDING PROBLEMS

(1) 60 Minute Fuses You have two lengths of fuse. Each will burn for exactly one hour. But the fuses are not necessarily identical and do not burn at a constant rate. There are fast- burning sections and slow-burning sections. How do you measure forty-five minutes using only the fuses and a lighter?

(2) Fit the numbers in the boxes: Write the numbers 1 to 8 in the boxes, so that no consecutive numbers are in adjacent boxes vertically, horizontally or diagonally. Each numbers should be used only once.

(3) Pick and Win Moonface and Bets are playing a game with white and black marbles. If a player picks a white marble, he wins. If he picks a black marble, he loses. There are two jars, one with 50 white marbles, and the other with 50 black marbles. Before picking, a player may distribute the marbles between the two jars in any way he wishes. All 100 marbles must be placed in the jars. Then the jars are shaken up, and the player will be blindfolded. He is then presented with one of the jars at random from which a marble is drawn at random. How should a player redistribute the marbles to maximize the probability that he picks a white marble and wins?

(4) Higher or lower solution Mrs. Stick had decided to test Bets’ love for the numbers. She brings two boxes with a number inside each box. The two numbers are different but unknown. Bets’ picks one box to open; reads the number inside; and then guesses if the number in the other box is larger or smaller. He will win if the guess is correct, and lose otherwise. Is there any way that Bets’ can win the game with more than 50% chances no matter what the two numbers are? Lecture 2 PUZZLES

Q.1. Add to get numbers Find the values of all alphabets to satisfy the condition given below, where each alphabet represent unique single digit numbers i.e. from 0-9. A B C D + E F G H I I I I

Q.2. After-Dinner Drink Alok, Bharat, and Chandra often eat dinner out. (1) Each orders either coffee or tea after dinner. (2) If Alok orders coffee, then Bharat orders the drink that Chandra orders. (3) If Bharat orders coffee, then Alok orders the drink that Chandra does’nt order. (4) If Chandra orders tea, then Alok orders the drink that Bharat orders. Who do you know always orders the same drink after dinner?

Q.3. Add to get the numbers: Alphabets A, B, C, D, E, F, G, H and I are single digit numbers between 0 to 9. Find the values of all alphabets such that it satisfies the expressions given below.

A A A A A A B B B D D D C C C E E E F G H I F G H I Q.4. Jailer and prisoners A team of 3 players, who are randomly, assigned hats that are equally likely to be white or black, under conditions such that: 1. Each team player can see the hats of the other team members, but cannot see their own hat. 2. Team members cannot communicate in any way among themselves. 3. Both colors of hats are present. The jailer asks them to tell the color of their own hat, and if all of them succeed in answering, he will release them, whereas if any one of them answers incorrectly, then he will kill all of them. All of them go and discuss for some time. And after they come back, he starts the test. Interestingly, each of them answers correctly and hence all are released. Lecture 3 PUZZLES

Q.1. Can you divide the number 45 into four parts such that when 2 is added to the first part, 2 is subtracted from the second part, 2 is multiplied by the third part and the fourth part is divided by 2. All the four results should be the same number.

Q. 2. Arjun, Bhim, and Nakul are brothers. (1) Arjun has exactly two brothers with grey eyes. (2) Bhim has exactly two brothers with grey or black eyes. (3) Nakul has exactly two brothers who do not have blue eyes. (4) At least one of the three has black eyes and at least one of the three has blue eyes. Whose eyes do you know the color of ?

Q.3. Consider 128 prisoners standing in a circle, numbered from 0 to 127 in clockwise order. The prisoner with number 0 is given a sword and he kills the prisoner next to him in clockwise order (i.e. prisoner number 1). Then, he gives the sword to the next prisoner (i.e. prisoner number 2). The prisoner 2 now cuts the head off prisoner number 3 and passes the sword to prisoner number 4 and so on. This keeps on happening till only 1 lucky guy remains. Now you have to tell us the number of the last man standing.

Q.4. One of Mr. Rahul, his wife, their son, and Mr. Rahul’s mother is a doctor and another is a lawyer. (1) If the doctor is younger than the lawyer, then the doctor and the lawyer are not blood relatives. (2) If the doctor is a woman, then the doctor and the lawyer are blood relatives. (3) If the lawyer is a man, then the doctor is a man. Whose occupation do you know surely?