On a man's tombstone, it is said that one sixth of his life was spent in childhood and one twelfth as a teenager. One seventh of his life passed between the time he became an adult and the time he married; five years later, his son was born. Alas, the son died four years before he did. He lived to be twice as old as his son did. How old did the man live to be?
Ans:84 years
You've been asked to buy 100 squeegies, using 100 dollars to do so. You may buy no more or less than 100 squeegies, and the total price must be exactly 100 dollars. There is no sales tax. Red squeegies cost $6.00. Yellow squeegies cost $3.00. Blue squeegies cost $0.10. How many of each must you buy?
Ans::
one red squeegie must be bought for $6, 29 yellow squeegies must be bought for $87, and 70 blue squeegies must be bought for $7.
Grass grows in a field at some rate r, where r is the units of grass grown per day. It is known that if 10 sheep are turned out in the field, the grass will be gone in 20 days. On the other hand, if 15 sheep are turned out in the field, the grass will be gone in 10 days. If 25 sheep are turned out in the field, when will the grass be gone?
Ans:: 25 sheep would consume all the grass in the field in 5 days
A clock is observed. The hour hand is exactly at the minute mark, and the minute hand is six minutes ahead of it. Later, the clock is observed again. This time, the hour hand is exactly on a different minute mark, and the minute hand is seven minutes ahead of it. How much time elapsed between the first and second observations?
Ans:The hour hand is exactly on a minute mark five times per hour -- on the hour, twelve minutes past the hour, twenty four minutes past, thirty six minutes past, and forty eight minutes past.
Let X be the number of hours, and Y be the number of minutes past the hour. When the hour hand is on a minute mark, the position of the hour hand is 5X + Y/12, and the position of the minute hand is Y. On the first occasion, Y = 5X + Y/12 + 6. This is equivalent to 60X = 11Y - 72. Since Y can only take one of the values in the set { 0, 12, 24, 36, 48 }, it can be determined that the only legal values for the equation are X = 1 and Y = 12. So the time is 1:12.
Similarly, the second occasion's equation is 60X = 11Y - 84. The only legal values here are X = 3 and Y = 24. So the time is 3:24.
Between 1:12 and 3:24, two hours and twelve minutes have elapsed.
Two trains travel toward each other on the same track, beginning 100 miles apart. One train travels at 40 miles per hour; the other travels at 60 miles an hour. A bird starts flight at the same location as the faster train, flying at a speed of 90 miles per hour. When it reaches the slower train, it turns around, flying the other direction at the same speed. When it reaches the faster train again, it turns around -- and so on. When the trains collide, how far will the bird have flown?
Ans:Since the trains are 100 miles apart, and the trains are traveling toward each other at 40 and 60 mph, the trains will collide in one hour. The bird will have been flying for an hour at 90 miles per hour at that point, so the bird will have traveled 90 miles.
A high school has a strange principal. On the first day, he has his students perform an odd opening day ceremony:
There are one thousand lockers and one thousand students in the school. The principal asks the first student to go to every locker and open it. Then he has the second student go to every second locker and close it. The third goes to every third locker and, if it is closed, he opens it, and if it is open, he closes it. The fourth student does this to every fourth locker, and so on. After the process is completed with the thousandth student, how many lockers are open?
Ans:The only lockers that remain open are perfect squares (1, 4, 9, 16, etc) because they are the only numbers divisible by an odd number of whole numbers; every factor other than the number's square root is paired up with another. Thus, these lockers will be "changed" an odd number of times, which means they will be left open. All the other numbers are divisible by an even number of factors and will consequently end up closed.
So the number of open lockers is the number of perfect squares less than or equal to one thousand. These numbers are one squared, two squared, three squared, four squared, and so on, up to thirty one squared. (Thirty two squared is greater than one thousand, and therefore out of range.) So the answer is thirty one.
Of three men, one always tells the truth, one always tells lies, and one answers "yes" or "no" randomly. Each man knows which one each of the others are. You may ask three yes/no questions, each of which may only be answered by one of the three men, after which you must be able to identify which man is which. How can you do it?
Ans: There are six possible scenarios. Let's call the first man A, the second man B, and the third man C. The six scenarios, then, are:
Scenario A B C
I Truthteller Liar Random Man
II Truthteller Random Man Liar
III Liar Truthteller Random Man
IV Liar Random Man Truthteller
V Random Man Truthteller Liar
VI Random Man Liar Truthteller
Follow these steps to determine which possibility listed above is correct:
1. Ask A, "Is B more likely to tell the truth than C?"
o If yes, go to step 2.
o If no, go to step 5.
2. Ask C, "Are you the random man?"
o If yes, go to step 3.
o If no, go to step 4.
3. Ask C, "Is A the truthteller?"
o If yes, then scenario V is the case.
o If no, then scenario II is the case.
4. Ask C, "Is A the liar?"
o If yes, then scenario IV is the case.
o If no, then scenario VI is the case.
5. Ask B, "Are you the random man?"
o If yes, go to step 6.
o If no, go to step 7.
6. Ask B, "Is A the truthteller?"
o If yes, then scenario VI is the case.
o If no, then scenario I is the case.
7. Ask B, "Is A the liar?"
o If yes, then scenario III is the case.
o If no, then scenario V is the case.
By following the steps above, you will only ever ask three questions in all, and the answers will determine the identities of the three men
Four switches can be turned on or off. One is the light switch for the incandescent overhead light in the next room, which is initially off, but you don't know which. The other three switches do nothing. From the room with the switches in it, you can't see whether the light in the next room is turned on or off. You may flip the switches as often and as many times as you like, but once you enter the next room to check on the light, you must be able to say which switch controls the light without flipping the switches any further. (And you can't open the door without entering, either!) How can you determine which switch controls the light?
Ans: Turn on switches 3 and 4 and wait fifteen minutes or so. Then turn switch 3 off, turn switch 2 on, and enter the room. If the bulb is dark and cool, switch 1 controls it. If the bulb is bright and cool, switch 2 controls it. If the bulb is dark and warm, switch 3 controls it. If the bulb is bright and warm, switch 4 controls it.
You've been sentenced to death in an obscure foreign country which has a strange law. Before the sentence is carried out, two papers -- one with "LIFE" written on it and one with "DEATH" written on it -- are folded up and placed in a hat. You are permitted to pick out one of the papers (without looking), and if you choose the one with "LIFE" written on it, you are set free. Otherwise, the death sentence is carried out. On this occasion, an enemy of yours, bent on your demise, has substituted the paper with "LIFE" written on it with another one with "DEATH" written on it. Now both the papers from which you have to pick out are written “DEATH” on them. This person informs you of what he has done and that you are doomed to die. You are not permitted to speak to anyone about this misdeed, nor will you have a chance to switch the papers or the hat yourself in time. How will you avoid certain death?
Ans: After you draw one of the papers, swallow it. The jailer will be forced to check the remaining paper to determine what the one you drew said. The jailer will of course see a paper with "DEATH" written on it, assume you drew the one with "LIFE" written on it, and set you free.
You have two slow-burning fuses, each of which will burn up in exactly one hour. They are not necessarily of the same length and width as each other, nor even necessarily of uniform width, so you can't measure a half hour by noting when one fuse is half burned. Using these two fuses, how can you measure 45 minutes?
Ans:
Light one fuse at both ends and, at the same time, light the second fuse at one end. When the first fuse has completely burned, you know that a half hour has elapsed, and, more relevantly, that the second fuse has a half hour left to go. At this time, light the second fuse from the other end. This will cause it to burn out in 15 more minutes. At that point, exactly 45 minutes will have elapsed.
You have twelve marbles. Eleven of the marbles are of equal weight, but one is heavier or lighter. You have a balancing scale you can use to find this marble and figure out if it weighs more or less than the others. What is the minimum number of weighings required to do this?
Ans: The problem can be solved in three weighings.
You have ten boxes, each of which contains nine balls. The balls in one box each weigh 0.9 pounds; the balls in all the other boxes weigh exactly one pound each. You have an accurate scale in front of you, with which you can determine the exact weight, in pounds, of any given set of balls. How can you determine which of the ten boxes contains the lighter balls with only one weighing?
Ans:
Number the boxes 0 through 9. Take zero balls from box 0, one ball from box 1, two balls from box 2, and so on. Weigh all these balls.
Now the required box number = (45-total weight) * 10
Abel, Mabel, and Caleb went bird watching. Each of them saw one bird that none of the others did. Each pair saw one bird that the third did not. And one bird was seen by all three. Of the birds Abel saw, two were yellow. Of the birds Mabel saw, three were yellow. Of the birds Caleb saw, four were yellow. How many yellow birds were seen in all? How many non-yellow birds were seen in all?
On your travels, three men stand at a fork in the road. You're not sure which fork you need to take, but each of the three men do. One of these people tells the truth, one always lies, and the third tells the truth sometimes and lies the other times. Each of the three men know each of the others, but you don't know who is who. If you could ask only one of the men (chosen at random, since you don't know which man is which) one yes/no question, what question would you ask to determine the road you wish to take?
Ans: Pick one of the men and ask, "If I were to ask you whether the left fork leads to where I'm going, and you chose to answer that question with the same degree of truth as you answer this question, would you then answer 'yes'?"
The truthteller will say "yes" if the left fork leads to where you're going and "no" otherwise. The liar will answer the same, since he will lie about where the left fork leads, and he will lie about lying. The third man may either lie or tell the truth about this one question, but either way he is behaving like either the truthteller or the liar and thus must correctly report the road to your destination.
Three humans and three monkeys (one big, two small) need to cross a river. But there is only one boat, and it can only hold two bodies (regardless of their size), and only the humans or the big monkey are strong enough to row the boat. Furthermore, the number of monkeys can never outnumber the number of humans on the same side of the river, or the monkeys will attack the humans. How can all six get across the river without anyone getting hurt?
Ans: The big monkey rows a small monkey over; the big monkey comes back. The big monkey rows the other small monkey over; the big monkey comes back. Two humans row over; a human and a small monkey come back. (Now two humans, the big monkey, and a small monkey are on the starting side of the river, and the third human and the second small monkey are on the destination side.) human and the big monkey row over; the human and a small monkey come back. Two humans row over; the big monkey rows back. (Now all the monkeys are on the starting side of the river, and all the humans are on the destination side.) The big monkey rows a small monkey over; the big monkey comes back. Then the big monkey rows the other small monkey over.
You have two cups, one containing orange juice and one containing an equal amount of lemonade. One teaspoon of the orange juice is taken and mixed with the lemonade. Then a teaspoon of this mixture is mixed back into the orange juice. Is there more lemonade in the orange juice or more orange juice in the lemonade?
Ans: There's the same amount of lemonade in the orange juice as orange juice in the lemonade. Each cup ends with the same volume of liquid that it started with, and there's still an equal amount of each juice between the two cups.
In a rectangular array of people, who will be taller: the tallest of the shortest people in each column, or the shortest of the tallest people in each row?
Ans: The shortest of the tallest people in each row will be taller than, or the same height as, the tallest of the shortest people in each column. There are four cases. The first is that the shortest of the tallest and the tallest of the shortest are the same person, so obviously in this case the shortest of the tallest and the tallest of the shortest would be the same height.
Three men stay at a hotel for the night. The innkeeper charges thirty dollars per room per night. The men rent one room; each pays ten dollars. The bellhop leads the men to their room. Later, the innkeeper discovers he has overcharged the men and asks the bellhop to return five dollars to them. On the way upstairs, the bellhop realizes that five dollars can't be evenly split among three men, so he decides to keep two dollars for himself and return one dollar to each man.At this point, the men have paid nine dollars each, totalling 27. The bellhop has two, which adds up to 29. Where did the thirtieth dollar go?
Answer: The mistake is in how the thirty dollars are accounted for. The two dollars that the bellhop has are part of the 27 the men have paid. A correct accounting of the money is that 27 dollars were paid and three dollars were not, totaling 30 dollars.
An Arab sheik is old and must will his fortune to one of his two sons. He makes a proposition. His two sons will ride their camels in a race, and whichever camel crosses the finish line last will win the fortune for its owner. During the race, the two brothers wander aimlessly for days, neither willing to cross the finish line. In desperation, they ask a wise man for advice. He tells them something; then the brothers leap onto the camels and charge toward the finish line. What did the wise man say?
Ans: The rules of the race were that the owner of the camel that crosses the finish line last wins the fortune. The wise man simply told them to switch camels.
A man is the owner of a winery who recently passed away. In his will, he left 21 barrels (seven of which are filled with wine, seven of which are half full, and seven of which are empty) to his three sons. However, the wine and barrels must be split so that each son has the same number of full barrels, the same number of half-full barrels, and the same number of empty barrels. Note that there are no measuring devices handy. How can the barrels and wine be evenly divided?
Two half-full barrels are dumped into one of the empty barrels. Two more half-full barrels are dumped into another one of the empty barrels. This results in nine full barrels, three half-full barrels, and nine empty barrels. Each son gets three full barrels, one half-full barrel, and three empty barrels.
322 hockey teams participate in an annual state tournament. The champion is chosen for this tournament by the usual elimination scheme. That is, the 322 teams are divided into pairs, and the two teams of each pair play against each other. The loser of each pair is eliminated, and the remaining teams are paired up again, etc. How many games must be played to determine a champion?
Answere::321
Isaac and Albert were excitedly describing the result of the Third Annual International Science Fair Extravaganza in Sweden. There were three contestants, Louis, Rene, and Johannes. Isaac reported that Louis won the fair, while Rene came in second. Albert, on the other hand, reported that Johannes won the fair, while Louis came in second.
In fact, neither Isaac nor Albert had given a correct report of the results of the science fair. Each of them had given one correct statement and one false statement. What was the actual placing of the three contestants?
Ans:
Johannes won
Rene came in second
Louis came in third.
A sheet of paper has statements numbered from 1 to 100.Statement N says "Exactly N of the statements on this sheet are false."
How many statements are true?
Ans:
1 statement is true.
The true statement is “Exactly 99 of statements on this sheet are false”
A rich man died.In his will, he has divided his gold coins among his 5 sons,5 daughters and a manager. According to his will:First give one coin to manager.1/5 th of remaining to the elder son. Now give one coin to the manager and 1/5 th of the remaining to second son and so on ..... After giving coins to 5th son ,divide the remaining coins among five daughters equally, All should get full coins. Find the minimum number of coins he has.
Ans:
3121
4 friends A,B,C and D were comparing the number of horses that they owned.
It was found that C has ten more horses than D.
If A gave one-third to B ,and B gave quater of what he held to C,
who then passed on a Fifth of his holding to D,they would all have an equal number of horses.
Find the minimum number of horses possessed by each of them.
Answer:
A 90
B 50
C 55
D 45
A man is on a search for Atlantis and comes upon an island where all the inhabitants know whether Atlantis is still around or not.However, all of the inhabitants are either Fairies or Trolls and they all use a spell to appear humanoid so you cannot tell which is which. And the Fairies always tell the truth and the Trolls always lie, but there is a slight complication, some of the Fairies have gone insane and always lie and some of the Trolls have also gone insane and always tell the truth.You must ask the first inhabitant that you come to ONE question and from that ONE question you must determine whether Atlantis is still around or not.
What is the question that you must ask?
There are two answers to it
1."Is the statement that you are reliable equivalent to the statement that atlantis is still around?"
2."Do you belive that the stament that you are a fairy is equivalent to the statement that Atlantis is still around."
A group of 1000 men are standing making a circle. They are numbered 1 to 1000.The person who is numbered 1 holds a sword. He kills the person numbered 2 and hand it to the person numbered 3....3 kills 4 and hands it over to 5 ...5 kills 6 and hands it over to 7....and so on and on and on.This killing spree continues till only one man is left.What would be his number???
Ans:
977
A, B, C, D, E, F, and G are having an argument about which day of the week it is. They speak as follows:
* A: The day after tomorrow is Wednesday.
* B: No, it is Wednesday today.
* C: You are both wrong; it is Wednesday tomorrow.
* D: Nonsense. Today is not Monday, not Tuesday and not Wednesday.
* E: I'm quite sure yesterday was Thursday.
* F: No, tomorrow is Thursday.
* G: All I know is that yesterday was not Saturday.
If only one of the remarks is true, what day of the week is it?
Answer:
Today is SUNDAY
Consider the sequence
Answere:
This sequence would never include the term '4'
Every next number describes the previous number1
11 (describes that there is a single '1' in the previous number)
21 (describes there are two 1's in the previous number)
1211 (describes there is a single 2, and a single 1 in the previous number)....and so on
For a '4' to be included, u will need to have 4 consecutive same digits. This is not possible in this sequence
Three sisters are identical triplets. The oldest by minutes is Sania, and Sania always tells anyone the truth. The next oldest is Saina, and Saina always will tell anyone a lie. Sana is the youngest of the three. She sometimes lies and sometimes tells the truth.
Answer:
Sana - left
Saina - middle
Sania - right
