A prisoner is told "If you tell a lie we will hang you; if you tell the truth we will shoot you." What can he say to save himself? Note that he must say something to save himself.
Answer:
He must say, "You will hang me." in order to escape from the clutches of death. Let us see how this works out. He cannot be hanged because he had predicted correctly and therefore uttered a true statement which calls for shooting him. He cannot be shot also since he had prophecied wrongly that he would be hanged. In either case, the statement uttered by the prisioner has put the authorities on the horns of a dilemma and the sentence can not be logically carried out thereby sending him scot-free.
92. COCK AND BULL STORY.
Tom and Jerry and the boys in the bar were exchanging old war stories. Tom offered one about how his grandfather led a battalion against a German division during World War I. Through brilliant manoeuvers, he defeated them and captured valuable territory. After the battle he was awarded a medal that was inscribed with:
"For Bravery, Daring and Leadership - World War I. From the Men of Battalion 8."
Jerry looked at Tom and said, "You really don't expect anyone to believe that cock and bull story, do you?" What's wrong with the story?
Answer:
World War I wasn't called "World War I" until World War II. Therefore he could not have been awarded the medal with the inscription containing the word World War I, especially just after the close of the warI. They may not possibly foresee for another world war to turn up then.
93. MAXIMUM PARTS.
How many parts can a circle be divided into drawing four straight lines? Give the maximum possible answer.
Answer:
The circle can be divided into 11 parts by drawing 4 straight lines. The trick is whenever you draw a line, it should cut all previously drawn lines and no more than 2 lines should pass through any intersection point. Hence whenver you draw N lines, the maximum possible parts are equal to 1 + (1 + 2 + 3 + 4 + 5 + ...... + N) = 1 + (N * (N + 1)) /2.
Post Scriptum:
You can see here how 4 straight lines divide a circle into maximum 11 parts.
94. CENTURY'S LAST DAY.
Which of the following day(s) can't be the last day of a century?
Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday. Justify your answer.
Answer:
The last day of a century can not be Tuesday, Thursday or Saturday. A normal year has 365 days whereas a leap year has 366 days. Every year which is divisible by 4 is called a leap year. Also, every 4th century is a leap year but no other century is a leap year. 1 normal year = 365 days = 52 weeks + 1 day 1 leap year = 366 days = 52 weeks + 2 day. Thus, a normal year has 1 odd day whereas a leap year has 2 odd days. 100 years = 76 normal years + 24 leap years = 76*[52 weeks + 1 day] + 24*[52 weeks + 2 day] = (76*52) weeks + 76 days + (24*52) weeks + 48 days = 5200 weeks + 124 days = 5217 weeks + 5 days i.e. 100 years contain 5 odd days Similarly, 200 years contain 10 odd days i.e. 3 odd days. 300 years contain 15 odd days i.e. 1 odd days. 400 years contain (20+1) odd days i.e. 0 odd days. Note that 400 years contain one more leap year. Also, we have Sunday for 0 odd day, Monday for 1 odd day, Tuesday for 2 odd days, and so on... Thus, last day of first century is Friday. (5 odd days). Last day of second century is Wednesday. (3 odd days) Last day of third century is Monday. (1 odd days) Last day of forth century is Sunday. (0 odd days) Since the order is repeating in successive cycles, the last day of a century can not be Tuesday, Thursday or Saturday.
95. MEASURE BY HOUR GLASS.
Can you clock the boiling of an egg for seven minutes, with a 9-minutes, 11-minutes and 14-minutes hourglass? If yes, then within how many minutes you can do this?
Answer: 1
16 minutes. Start all the hourglasses together. When the sand stops running in the 9-minute hourglass, the 11-minute hourglass will have 2 minutes remaining whereas the 14-minute hourglass will have 5 minutes remaining. Now, turn the 14-minute hourglass on its side and simultaneously drop the egg. When the sand stops running in 11-minute hourglass, straighten the 14-minute hourglass. Thus, the whole process takes just 16 minutes.
Answer: 2
18 minutes. Start all the hourglasses together. When the sand stops running in the 9-minute hourglass, turn the 14-minute hourglass over. When the sand stops running in 11-minute hourglass, turn again the 14-minute hourglass and simultaneously drop the egg. When the sand stops in the 14-minute hourglass, seven minutes will have elapsed. Thus, the whole process takes 18 minutes.
96. ROYAL ESCAPE.
A Queen (78kg), the Prince (36kg) and the King (42kg) are stuck at the top of a tower. A pulley is fixed to the top of the tower. Over the pulley is a rope with a basket on each end. One basket has a 30kg stone in it. The baskets are enough for 2 people or 1 person and the stone. For safety's sake there can't be more than a 6kg difference between the weights of the baskets if someone's inside. How do the people all escape?
Answer:
Basket 1 Basket 2
Stone up Prince down
King down Prince up
nothing up Stone down
Queen down Stone and King up
nothing up Stone down
Prince down Stone up
nothing up Stone down
King down Prince up
Stone up Prince down
97. IMPOSSIBLE.
Question: 1.
Apples are packed in boxes of 8 and 15. What is the biggest number of apples that cannot be packed using the above two boxes?
Question: 2.
A country only has 5p and 7p coins. Make a list of prices that you could give exact money for. What is the highest prices that you couldn't give exact money for?
Answer:
"Given integers 'a' and 'b' the biggest number that can't be expressed in the form ia + jb is (ab - a - b). Using this the answers easily turn out to be 97 and 23 for questions 1 and 2 respectively.
98. HOW MUCH IS THE LOSS?
A cheat goes to a footwear shop and buys a product for 12 dollars paying with a 20 dollar note. As the seller did not have necessary change, he changes it from the next door shop and gives the cheat the balance 8 dollar and the product. After certain time, the second shop owner returns the 20 dollar note, saying that it is counterfeit. Now the poor first seller has to shell out another 20 dollar to the second shop owner. Besides, for nothing, he has sold the product whose value is 12 dollar and also gave the balance 8 dollar to the cheat. Now the question is how much is the exact loss incurred to the shop owner?
Answer:
Many people fall prey to this simple, beautiful problem saying that the loss is only 40. Because the shop owner has sold the cheat the product whose value is 12 and also given him 8, besides he has to pay another 20 to the second shop owner. Some might think that the loss is only 32, because he had returned the balance 8, not from his own pocket but from the change given by the second shop owner. Therefore 40-8=32 is the actual loss. To cut the long story short, the loss is only 20 dollars. You forget the story of second shop owner's transaction and try to think afresh in the following way: For a counterfeit 20 dollar, he had delivered the product (value 12 dollors) and lost 8 by way of giving him the balance.
99. HOW TO FIND DIRECTION?
Two men stand at a fork in the road. One fork leads to Town A; the other fork leads to Town B. One of these people always answers the truth to any yes/no question which is asked of him. The other always lies when asked any yes/no question. Both of them knew which road leads to which? By asking one yes/no question, can you determine the road to Town A?
Answer:
The fact that there are two men is a red herring - you only need one of them. Ask either of them the question:
"If I ask you if the left fork leads to Town A, will you answer 'yes'?" If the person asked is a truthteller, he will answer "yes" if the left fork leads to Town A, and "no" otherwise. In the event of the person asked is a liar and if the left road does not lead to Town A, still the liar will tell "yes". So irrespective of whether the person is a truthteller or a liar, if he says "yes", we can safely take the left road to Town A. If the answer to the question is a "no", take the other one, the right road.
Note:
In is interesting to note that the above problem can be formulated into a different shape by telling that only one person standing at the fork, whose nature (i.e. truthteller or a liar) we don't know and still can determine which road leads to Town A, by just asking one question.
100. TRUTH TELLER OR LIAR?
In some remote Island, there lived two kinds of people -- knights and knaves. The knights always tell the truth, but the knaves always tell a lie. John and Bill are residents of that Island. Question 1: John says: We are both knaves. Who is who?
Question 2: John: If Bill is a knave then I'm a knight. Bill: We are different. Who is who?
Question 3: Logician: Are you both knights? John: Yes or No. Logician: Are you both knaves? John: Yes or No. Who is who?
Solution to Question 1:
We can use Boolean algebra to deduce who's who as follows: Let J be true if John is a knight and let B be true if Bill is a knight. Now, either John is a knight and what he said was true, or John is not a knight and what he said was false. Translating that into Boolean algebra, we get:
(J^(J>^B>)) v (J>^(J>^B>)>) tautology
Simplification process:
(J^(J>^B>)) v (J>^(J>^B>)>)
false v (J>^(J>^B>)>); J^J> = contradiction
(J>^(J>^B>)>); contradiction v X=X
(J>^(J v B)); by de morgan theorem
((J>^J) v (J>^B))
(J>^B) = tautology
Therefore John is a knave and Bill is a knight. Although most people can solve this puzzle without using Boolean algebra, the example still serves as a powerful testament of the power of Boolean algebra in solving logic puzzles.