1.Boston United's latest player lives on the 13th floor of a tower block. Every morning he takes the lift down to the ground floor and leaves the building. When he returns home in the evening, if there is someone else in the lift or it's raining he goes straight back to his floor directly. However, if there is nobody else in the lift or it hasn't rained he goes up to the 10th floor and walks up the remaining three flights of stairs. He hates walking up stairs so why does he do it?
2.There are 2 identical strings. If you light one of the strings at its end, it will take exactly one hour for it to finish burning completely. The string will not burn evenly - it is thicker in some places, thinner in others. For example, the string may not be half consumed exactly 30 minutes from lighting it at one end. You have no other means of telling time, and you want to know when exactly 45 minutes have passed. All that you have is a lighter and these 2 identical strings. What is the most accurate method you can use, given these conditions?
3.A water lily growing in a circular pond doubles in size every day. It takes thirty days to cover the whole pond. How long does it take to cover half the pond?
Tuesday, November 27, 2007
Needs a Strong Logic
There was a good job going in the office and the boss could not decide which of the three candidates should have it, each of them being worthy of it and all of them very bright indeed. So he set them a problem and the one who solved it would get the job. He showed them five discs, three black and two white and said: ?I?m going to put a disc on the forehead of each of you. You will be able to see the others discs but not your own. There will be no talking. By pure deduction you will have to work out what colour disc you have, and the one who does so gets the job.? He withheld the two white discs and put a black one on each of them. After a time one of the men stepped forward and successfully claimed the job. How did he figure out that he had a black disc on?
COMMON PHRASES
Example
1001 A- N- : 1001 Arabian Nights
366 D- in a L- Y- : 366 Days in a Leap Year
1.11 P- in a F- T-
2.64 S- on a C- B-
3.20 N- on a D- B-
4.26 L- of the A-
5.88 P- K-
6.49=S- S-
7.60 M- in an H-
8.24 H- in a D-
9.11 P- in a F- T-
10.64 S- on a C- B-
11.20 N- on a D- B-
12.26 L- of the A-
13.88 P- K-
14.49=S- S-
15.60 M- in an H-
1001 A- N- : 1001 Arabian Nights
366 D- in a L- Y- : 366 Days in a Leap Year
1.11 P- in a F- T-
2.64 S- on a C- B-
3.20 N- on a D- B-
4.26 L- of the A-
5.88 P- K-
6.49=S- S-
7.60 M- in an H-
8.24 H- in a D-
9.11 P- in a F- T-
10.64 S- on a C- B-
11.20 N- on a D- B-
12.26 L- of the A-
13.88 P- K-
14.49=S- S-
15.60 M- in an H-
HANDSOME SEQUENCES
1.What is the next letter in the following sequences.
W I T N L I T F ? (Clue - look up!)
2.Looking back on it, this series makes perfect sense.
8 65 293 4472 80291 ?
3.Timing is everything, & this is true every day of the week.
6 6 7 9 8 6 ?
4.A B D O P ? (Clue - this one's not about football)
5.It’s not the numbers which always makes sequence, sometimes alphabets also do
10, 9,60,90,70,?
6. I suppose I should start by saying hello.
23 5 12 3 15 13 ?
7. My primary objective is cumulative multiplication. I know, it's an odd objective.
3 10 21 44 65 102 ?
8.sometimes numbers are no more than they appear to be.
3 3 5 4 4 3 5 5 4 ?
9.At this point, I'm afraid you will accuse me of being fractious.
5 6 7 8 8 8 8 8 ?
10.If you have double vision, sometimes things appear unbalanced.
31 53 97 275 451 ?
11.Occasionally things are presented to us in an unusual, yet completely logical order.
2 5 12 23 30 17 8 ?
W I T N L I T F ? (Clue - look up!)
2.Looking back on it, this series makes perfect sense.
8 65 293 4472 80291 ?
3.Timing is everything, & this is true every day of the week.
6 6 7 9 8 6 ?
4.A B D O P ? (Clue - this one's not about football)
5.It’s not the numbers which always makes sequence, sometimes alphabets also do
10, 9,60,90,70,?
6. I suppose I should start by saying hello.
23 5 12 3 15 13 ?
7. My primary objective is cumulative multiplication. I know, it's an odd objective.
3 10 21 44 65 102 ?
8.sometimes numbers are no more than they appear to be.
3 3 5 4 4 3 5 5 4 ?
9.At this point, I'm afraid you will accuse me of being fractious.
5 6 7 8 8 8 8 8 ?
10.If you have double vision, sometimes things appear unbalanced.
31 53 97 275 451 ?
11.Occasionally things are presented to us in an unusual, yet completely logical order.
2 5 12 23 30 17 8 ?
Friday, December 08, 2006
confused bank teller
A confused bank teller transposed the dollars and cents when he cashed a check for Ms Smith, giving her dollars instead of cents and cents instead of dollars. After buying a newspaper for 50 cents, Ms Smith noticed that she had left exactly three times as much as the original check. What was the amount of the check? (Note: 1 dollar = 100 cents.)
Solution to puzzle : Confused bank teller
Solution by Diophantine Equation
Let x be the number of dollars in the check, and y be the number of cents.Then 100y + x - 50 = 3(100x + y).Therefore 97y - 299x = 50.
A standard solution to this type of Diophantine equation uses the Euclidean algorithm.
The steps of the Euclidean algorithm for calculating the greatest common divisor (gcd) of 97 and 299 are as follows:
299 = 3 × 97 + 8
97 = 12 × 8 + 1
This shows that gcd(97,299) = 1.
To solve 97y - 299x = gcd(97,299) = 1, we can proceed backwards, retracing the steps of the algorithm as follows:
1
= 97 - 8 × 12
= 97 - (299 - 3 × 97) × 12
= 37 × 97 - 12 × 299
Therefore a solution to 97y - 299x = 1 is y = 37, x = 12.Hence a solution to 97y - 299x = 50 is y = 50 × 37 = 1850, x = 50 × 12 = 600.It can be shown that all integer solutions of 97y - 299x = 50 are of the form y = 1850 + 299k, x = 600 + 97k, where k is any integer.
In this case, because x and y must be between 0 and 99, we choose k = -6.This gives y = 56, x = 18.So the check was for $18.56.
Solution to puzzle : Confused bank teller
Solution by Diophantine Equation
Let x be the number of dollars in the check, and y be the number of cents.Then 100y + x - 50 = 3(100x + y).Therefore 97y - 299x = 50.
A standard solution to this type of Diophantine equation uses the Euclidean algorithm.
The steps of the Euclidean algorithm for calculating the greatest common divisor (gcd) of 97 and 299 are as follows:
299 = 3 × 97 + 8
97 = 12 × 8 + 1
This shows that gcd(97,299) = 1.
To solve 97y - 299x = gcd(97,299) = 1, we can proceed backwards, retracing the steps of the algorithm as follows:
1
= 97 - 8 × 12
= 97 - (299 - 3 × 97) × 12
= 37 × 97 - 12 × 299
Therefore a solution to 97y - 299x = 1 is y = 37, x = 12.Hence a solution to 97y - 299x = 50 is y = 50 × 37 = 1850, x = 50 × 12 = 600.It can be shown that all integer solutions of 97y - 299x = 50 are of the form y = 1850 + 299k, x = 600 + 97k, where k is any integer.
In this case, because x and y must be between 0 and 99, we choose k = -6.This gives y = 56, x = 18.So the check was for $18.56.
puzzles for school children
Q1: Each child in a family has at least 5 brothers and 4 sisters. What is the smallest number of children the family might have?
Q2: Louise runs the first half of a race at 5 miles per hour. Then she picks up her pace and runs the last half of the race at 10 miles per hour. What is her average speed on the course?
Q3:what is ?
8
2 5 2
1 2 4 2 1
1 2 1 3 1 2 1
1 2 1 1 ? 1 1 2 1
Q4: How Many Days?Froggie fell down a 10-foot well. He cannot hop out. He has to climb out. He climbs three feet a day, but during the night, while resting, he slips back two feet. At this rate, how many days will it take Froggie to climb out of the well?
Q5: How Many Marbles?
Marta distributed 100 marbles among five bags.
Bag #1 and Bag #2 together contain 52 marbles.Bag #2 and Bag #3 together contain 43 marbles.Bag #3 and Bag #4 together contain 34 marbles.Bag #4 and Bag #5 together contain 30 marbles. How many marbles are there in each bag?
Q6: How Many Students?
A new school has opened with fewer than 500 students. One-third of the students is a whole number. So are one-fourth, one-fifth, and one-seventh of the students. How many students go to this school?
Q7: Pick a Pair
Ben has socks in five different colors: two pairs of blue socks, two pairs of black, three pairs of brown, four pairs of green, and four pairs of white. Ben, who is not very neat, doesn't bother to pair up his socks when he puts them away. He just throws them in the drawer. Now Ben is packing to go away for the weekend, but there's been a power failure and he can't see the socks in his drawer.
How many socks does he have to take out of his drawer to be sure he has at least two that will make a pair?
Q8: Sale!
An online shopping site reduced the price of one computer model by 25 percent for a sale. By what percentage of the sales price must it be increased to put the computer model back at its original price?
Q9: Which Way?
Once a boy was walking down the road, and came to a place where the road divided in two, each separate road forking off in a different direction.
A girl was standing at the fork in the road. The boy knew that one road led to Lieville, a town where everyone always lied, and the other led to Trueville, a town where everyone always told the truth. He also knew that the girl came from one of those towns, but he didn't know which one.
Can you think of a question the boy could ask the girl to find out the way to Trueville?
Q2: Louise runs the first half of a race at 5 miles per hour. Then she picks up her pace and runs the last half of the race at 10 miles per hour. What is her average speed on the course?
Q3:what is ?
8
2 5 2
1 2 4 2 1
1 2 1 3 1 2 1
1 2 1 1 ? 1 1 2 1
Q4: How Many Days?Froggie fell down a 10-foot well. He cannot hop out. He has to climb out. He climbs three feet a day, but during the night, while resting, he slips back two feet. At this rate, how many days will it take Froggie to climb out of the well?
Q5: How Many Marbles?
Marta distributed 100 marbles among five bags.
Bag #1 and Bag #2 together contain 52 marbles.Bag #2 and Bag #3 together contain 43 marbles.Bag #3 and Bag #4 together contain 34 marbles.Bag #4 and Bag #5 together contain 30 marbles. How many marbles are there in each bag?
Q6: How Many Students?
A new school has opened with fewer than 500 students. One-third of the students is a whole number. So are one-fourth, one-fifth, and one-seventh of the students. How many students go to this school?
Q7: Pick a Pair
Ben has socks in five different colors: two pairs of blue socks, two pairs of black, three pairs of brown, four pairs of green, and four pairs of white. Ben, who is not very neat, doesn't bother to pair up his socks when he puts them away. He just throws them in the drawer. Now Ben is packing to go away for the weekend, but there's been a power failure and he can't see the socks in his drawer.
How many socks does he have to take out of his drawer to be sure he has at least two that will make a pair?
Q8: Sale!
An online shopping site reduced the price of one computer model by 25 percent for a sale. By what percentage of the sales price must it be increased to put the computer model back at its original price?
Q9: Which Way?
Once a boy was walking down the road, and came to a place where the road divided in two, each separate road forking off in a different direction.
A girl was standing at the fork in the road. The boy knew that one road led to Lieville, a town where everyone always lied, and the other led to Trueville, a town where everyone always told the truth. He also knew that the girl came from one of those towns, but he didn't know which one.
Can you think of a question the boy could ask the girl to find out the way to Trueville?
Thursday, August 17, 2006
"Enjoy The Puzzles"
Q1:
A person who was making a list of population of NOIDA came to RAM’s house and that man wants to record the age of all people staying with RAM. That man was RAM’s childhood friend meeting after a longtime.
RAM’S FRIEND: "How have you been?"
RAM: "Great! I got married and I have three daughters now.
"RAM’S FRIEND: "Really? How old are they?"
RAM: "Well, the product of their ages is 72, and the sum of their ages is the same as the number on that building over there..."
RAM’S FRIEND: "Right, ok... Oh wait... Hmm, I still don't know."
RAM: "Oh sorry, the oldest one just started to play the piano."
RAM’S FRIEND: "Wonderful! My oldest is the same age!"
Q2:
Five pirates discover a chest full of 100 gold coins. The pirates are ranked by their years of service, Pirate 5 having five years of service, Pirate 4 four years, and so on down to Pirate 1 with only one year of deck scrubbing under his belt. To divide up the loot, they agree on the following:
The most senior pirate will propose a distribution of the booty. All pirates will then vote, including the most senior pirate, and if at least 50% of the pirates on board accept the proposal, the gold is divided as proposed. If not, the most senior pirate is forced to walk the plank and sink to Davy Jones’ locker. Then the process starts over with the next most senior pirate until a plan is approved.
Remember that these pirates are not ordinary people they are extremely intelligent and greedy, they are also perfectly rational and know exactly how the others will vote in every situation. Emotions play no part in their decisions.
The most senior pirate thinks for a moment and then proposes a plan that maximizes his gold, and which he knows the others will accept. How does he divide up the coins?
Q3:
The warden meets with 23 new prisoners when they arrive. He tells them, "You may meet today and plan a strategy. But after today, you will be in isolated cells and will have no communication with one another.
"In the prison is a switch room, which contains two light switches labeled A and B, each of which can be in either the 'on' or the 'off' position. I am not telling you their present positions. The switches are not connected to anything.
"After today, from time to time whenever I feel so inclined, I will select one prisoner at random and escort him to the switch room. This prisoner will select one of the two switches and reverse its position. He must move one, but only one of the switches. He can't move both but he can't move none either. Then he'll be led back to his cell
"No one else will enter the switch room until I lead the next prisoner there, and he'll be instructed to do the same thing. I'm going to choose prisoners at random. I may choose the same guy three times in a row, or I may jump around and come back.
"But, given enough time, everyone will eventually visit the switch room as many times as everyone else. At any time anyone of you may declare to me, 'We have all visited the switch room.' and be 100% sure.
"If it is true, then you will all be set free. If it is false, and somebody has not yet visited the switch room, you will be fed to the alligators."
What is the strategy they come up with so that they can be free?
Q4:
you are presented with three doors (door 1, door 2, door 3). one door has a million dollars behind it. the other two have goats behind them. you do not know ahead of time what is behind any of the doors.
monty asks you to choose a door. you pick one of the doors and announce it. monty then counters by showing you one of the doors with a goat behind it and asks you if you would like to keep the door you chose, or switch to the other unknown door.
should you switch? if so, why? what is the probability if you don't switch? what is the probability if you do.
Q5:
There is a pile of N (can be Even or Odd) coins placed on a table, in which K coins head upward. Can you make two piles of coin out of this pile having equal number of heads upward? But you can’t see which coin is heading upward, you can just count coins. No restriction on K
Q6:
"a line of 100 airline passengers is waiting to board a plane. they each hold a ticket to one of the 100 seats on that flight. (for convenience, let's say that the nth passenger in line has a ticket for the seat number n.)
unfortunately, the first person in line is crazy, and will ignore the seat number on their ticket, picking a random seat to occupy. all of the other passengers are quite normal, and will go to their proper seat unless it is already occupied. if it is occupied, they will then find a free seat to sit in, at random.
what is the probability that the last (100th) person to board the plane will sit in their proper seat (#100)?"
Q7:
"at one point, a remote island's population of chameleons was divided as follows:
13 red chameleons
15 green chameleons
17 blue chameleons
each time two different colored chameleons would meet, they would change their color to the third one. (i.e.. If green meets red, they both change their color to blue.) is it ever possible for all chameleons to become the same color? why or why not?"
Q8:
You have 12 coins. One of them is counterfeit. All the good coins weigh the same, while the counterfeit one weights either more or less than a good coin. Your task is to find the counterfeit coin using a balance-scale in 3 weighs. Moreover, you want to say whether the coin weighs more or less. (have patience b’coz its solvable)
Q9:
There are 10 ball producing machines out of which 9 machines produces 10gm balls and the remaining one produces 11gm balls, you are given with a weighing balance with all kinds of weights so that u can measure any weight you like, you have to identify which machine produces the 11gm balls but you can weigh only once. You have sufficient number of balls from each machine.
Q10:
you have $10,000 dollars to place a double-or-nothing bet on India in the Pepsi cup (max 7 games, series is over once a team wins 4 games). Unfortunately, you can only bet on each individual game, not the series as a whole. How much should you bet on each game, so that, if the yanks win the whole series, you expect to get 20k, and if they lose, you expect 0? Basically, you know that there may be between 4 and 7 games, and you need to decide on a strategy so that whenever the series is over, your final outcome is the same as an overall double-or-nothing bet on the series.
A person who was making a list of population of NOIDA came to RAM’s house and that man wants to record the age of all people staying with RAM. That man was RAM’s childhood friend meeting after a longtime.
RAM’S FRIEND: "How have you been?"
RAM: "Great! I got married and I have three daughters now.
"RAM’S FRIEND: "Really? How old are they?"
RAM: "Well, the product of their ages is 72, and the sum of their ages is the same as the number on that building over there..."
RAM’S FRIEND: "Right, ok... Oh wait... Hmm, I still don't know."
RAM: "Oh sorry, the oldest one just started to play the piano."
RAM’S FRIEND: "Wonderful! My oldest is the same age!"
Q2:
Five pirates discover a chest full of 100 gold coins. The pirates are ranked by their years of service, Pirate 5 having five years of service, Pirate 4 four years, and so on down to Pirate 1 with only one year of deck scrubbing under his belt. To divide up the loot, they agree on the following:
The most senior pirate will propose a distribution of the booty. All pirates will then vote, including the most senior pirate, and if at least 50% of the pirates on board accept the proposal, the gold is divided as proposed. If not, the most senior pirate is forced to walk the plank and sink to Davy Jones’ locker. Then the process starts over with the next most senior pirate until a plan is approved.
Remember that these pirates are not ordinary people they are extremely intelligent and greedy, they are also perfectly rational and know exactly how the others will vote in every situation. Emotions play no part in their decisions.
The most senior pirate thinks for a moment and then proposes a plan that maximizes his gold, and which he knows the others will accept. How does he divide up the coins?
Q3:
The warden meets with 23 new prisoners when they arrive. He tells them, "You may meet today and plan a strategy. But after today, you will be in isolated cells and will have no communication with one another.
"In the prison is a switch room, which contains two light switches labeled A and B, each of which can be in either the 'on' or the 'off' position. I am not telling you their present positions. The switches are not connected to anything.
"After today, from time to time whenever I feel so inclined, I will select one prisoner at random and escort him to the switch room. This prisoner will select one of the two switches and reverse its position. He must move one, but only one of the switches. He can't move both but he can't move none either. Then he'll be led back to his cell
"No one else will enter the switch room until I lead the next prisoner there, and he'll be instructed to do the same thing. I'm going to choose prisoners at random. I may choose the same guy three times in a row, or I may jump around and come back.
"But, given enough time, everyone will eventually visit the switch room as many times as everyone else. At any time anyone of you may declare to me, 'We have all visited the switch room.' and be 100% sure.
"If it is true, then you will all be set free. If it is false, and somebody has not yet visited the switch room, you will be fed to the alligators."
What is the strategy they come up with so that they can be free?
Q4:
you are presented with three doors (door 1, door 2, door 3). one door has a million dollars behind it. the other two have goats behind them. you do not know ahead of time what is behind any of the doors.
monty asks you to choose a door. you pick one of the doors and announce it. monty then counters by showing you one of the doors with a goat behind it and asks you if you would like to keep the door you chose, or switch to the other unknown door.
should you switch? if so, why? what is the probability if you don't switch? what is the probability if you do.
Q5:
There is a pile of N (can be Even or Odd) coins placed on a table, in which K coins head upward. Can you make two piles of coin out of this pile having equal number of heads upward? But you can’t see which coin is heading upward, you can just count coins. No restriction on K
Q6:
"a line of 100 airline passengers is waiting to board a plane. they each hold a ticket to one of the 100 seats on that flight. (for convenience, let's say that the nth passenger in line has a ticket for the seat number n.)
unfortunately, the first person in line is crazy, and will ignore the seat number on their ticket, picking a random seat to occupy. all of the other passengers are quite normal, and will go to their proper seat unless it is already occupied. if it is occupied, they will then find a free seat to sit in, at random.
what is the probability that the last (100th) person to board the plane will sit in their proper seat (#100)?"
Q7:
"at one point, a remote island's population of chameleons was divided as follows:
13 red chameleons
15 green chameleons
17 blue chameleons
each time two different colored chameleons would meet, they would change their color to the third one. (i.e.. If green meets red, they both change their color to blue.) is it ever possible for all chameleons to become the same color? why or why not?"
Q8:
You have 12 coins. One of them is counterfeit. All the good coins weigh the same, while the counterfeit one weights either more or less than a good coin. Your task is to find the counterfeit coin using a balance-scale in 3 weighs. Moreover, you want to say whether the coin weighs more or less. (have patience b’coz its solvable)
Q9:
There are 10 ball producing machines out of which 9 machines produces 10gm balls and the remaining one produces 11gm balls, you are given with a weighing balance with all kinds of weights so that u can measure any weight you like, you have to identify which machine produces the 11gm balls but you can weigh only once. You have sufficient number of balls from each machine.
Q10:
you have $10,000 dollars to place a double-or-nothing bet on India in the Pepsi cup (max 7 games, series is over once a team wins 4 games). Unfortunately, you can only bet on each individual game, not the series as a whole. How much should you bet on each game, so that, if the yanks win the whole series, you expect to get 20k, and if they lose, you expect 0? Basically, you know that there may be between 4 and 7 games, and you need to decide on a strategy so that whenever the series is over, your final outcome is the same as an overall double-or-nothing bet on the series.
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