1.18,46,94,63,52, ….
2.613452,25431,1342,231....
3.11,2,4,16,37,58...
4.0,9,26,65...
Wednesday, October 8, 2008
Disappointment
Vengeance went to chill out at the local club last night. However, due to an invitation only event the entry was restricted. Only people who spoke the correct password to the doorman were allowed to enter.
Vengeance was not aware of the password, so he waited by the door and listened. A guest knocked on the door and the doorman said, "Twelve."
The guest replied, "Six " and was let in.
A second guest came to the door and the doorman said, "Six."
The guest replied, "Three" and was let in.
At this moment Vengeance thought that he had cracked the code and walked up to the door. The doorman said ,"Ten" to which Vengeance replied, "Five."
Unfortunately for Vengeance, he was not let in.
What should have he said to gain entry to the club?
Vengeance was not aware of the password, so he waited by the door and listened. A guest knocked on the door and the doorman said, "Twelve."
The guest replied, "Six " and was let in.
A second guest came to the door and the doorman said, "Six."
The guest replied, "Three" and was let in.
At this moment Vengeance thought that he had cracked the code and walked up to the door. The doorman said ,"Ten" to which Vengeance replied, "Five."
Unfortunately for Vengeance, he was not let in.
What should have he said to gain entry to the club?
Cricket crazy
Honesty and Perseverance were watching a game of cricket when an interesting scenario surfaced. The two batsmen X and Y were playing on 98 runs and 94 runs respectively. Both wanted to score a century but their team required only 3 runs to win the match with only 2 balls remaining. It is given that X was on strike and both eventually made a century to win the match. There were no extra deliveries (no-balls/wide) bowled.
How is this possible?
How is this possible?
Missing Jacket
Roger and Rafael visited a small town in France. While coming back , Roger forgot his Jacket in a bus. When he reported this to the bus company, the company asked him the bus number , which he vaguely remembered but he noted a peculiar property of the bus number. The number plate showed that the bus number was a perfect square and also if the plate was turned upside down, the number would still be perfect square. The bus company informed him they had only 500 buses with numbers from 1 to 500 . How was Roger able to deduce the bus number and what was the bus number ?
Free hit
In 1990, a person is 15 years old. In 1995 that same person is 10 years old. How is this possible?
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IIT Puzzles
1. Suppose a clock's seconds hand is exactly on a second’s mark (one of
the sixty) and exactly 22 second marks ahead of the hour hand. What is
the time?
2. Nowadays as the security threat is rising, number locks are becoming
common.
Say you have a number lock having number keys from 1 to 5. You are
allowed to press either single keys or a pair of number keys simultaneously.
Also you cannot press 3 keys simultaneously or repeat a key which was
pressed previously. The order in which the keys were pressed matters but
when a pair is pressed simultaneously, there is no order between them i.e.
[(12)] is the same as [(21)].
Let’s call a key combination satisfying all these conditions as legal
combinations.
Find the number of such legal combinations.
3. You are given some matches, a thread and a pair of scissors. The thread
burns irregularly and takes 1 hour to burn from one end to the other. It has
a symmetry property that the burn rate at a distance x from the left end is
same as the burn rate at a distance x from the right end. What is the
minimum time interval you can measure accurately using the above?
Explain the method.
4. There are 26 stones having weights between 1kg and 26kg, not
necessarily distinct. All the weights are whole nos. All you have is a pan
balance. What is the minimum no. of known weights (whole numbered)
required to find the weight of each of the stones and what are they?
*Conventional methods might not always be the best ones
5.If 1 ----> 3
2 ----> 3
3 ----> 5
4 ---->4
5 ----> 4
6 ----> 3
7 ----> 5
8 ----> 5
9 ----> 4
10 ----> A . Find A.
Divide a regular hexagon into B (= A^2) pieces of two types (By types, we
mean two sets of geometric figures. Eg, a set of x congruent triangles and
a set of y congruent rectangles, where B=x+y) so that they can be
rearranged to form a single equilateral triangle.
Find x, y and the shape of the geometric figures.
(Describe in words, the division of the hexagon and formation of the
equilateral triangle)
6.You and 2 other people have numbers written on your foreheads. You are
all told that the numbers on your foreheads are prime and that they form
a triangle with a prime perimeter. You see 5 and 7 on the other 2 people.
All three of you claim you do not know the number on your forehead,
starting from you and now again it is your turn. Can you guess the number
on your forehead? Justify your answer.
7.A deck of cards has: 9 aces of spades, 8 deuces of spades, 7 threes… 2
eights and 1 nine of spade: 45 cards in total. The deck is shuffled and a
card is drawn. You should guess it by asking yes-no questions.
How can you minimize the number of questions that you will probably
have to ask? How will your answer differ
- If the deck is replaced by numbers one to one million?
- If the person who answers is permitted to lie twice?
8.Generally a ray of light can reflect many times between 2 ordinary line
mirrors. Now we introduce the condition that on each line mirror there is
only one point of reflection i.e. any ray can get reflected only at this
particular point on that mirror. Now let us call such mirrors as point mirrors.
But the laws of reflection are still dependent on the orientation of the line.
We find a maximum of 3 reflections for 2 mirrors. What is the maximum no.
of reflections for (a) 4 mirrors (b) 5 mirrors.
9.The Good, The Bad and The Ugly get into a pistol duel under unusual terms. They
draw lots and determine the order in which they start firing (who first, who second
and who third). They also decide to use the same type of pistol and bullets. Then,
they take up their positions at the corners of an equilateral triangle. They come to an
agreement that each of them will fire single shots, in turn, and continue in the same
cyclic order until two of them are dead. At his turn, the one who is firing may aim
wherever he pleases. It is also well known that The Bad always hits his target, The
Ugly hits his target three out of four turns and The Good manages only one out of
two. Assume that all of them adopt the best strategy in the duel and no one is killed
by an arbitrary shot not intended for him.
Who has the best chance to survive?
What are the exact survival probabilities of the three men?
How will your answer differ if the triangle is not equilateral and, in turns, they start
shooting bullets at regular intervals of time? Explain.
10.Gandalf and the Fellowship, finding their way through the Mines of Moria
reach a spot where they find too many paths branching out. Some
branches lead out of the Mines safely while others do not. No one knows
beforehand which branches are safe and which are not. They are
suddenly confronted by a Balrog. Panic settles in and Gandalf and the
Fellowship are separated. Both of them randomly select a distinct branch
from the set of pathways and pursue it. It is an even-money bet that both
Gandalf and the Fellowship have chosen safe pathways.
What may be the possible number of total safe pathways?
11.T-Bag is left stranded in a desolate desert area in Panama with just a
scooter and a broken hand. He discovers that there is an unlimited supply
of petrol at that particular place. He has to traverse a distance of 1000
miles and knows that there is no other petrol source on the way. His
scooter can carry petrol to go 500 miles (say L liters) and he can build his
own refueling stations at any spot on the way.
What is the minimum amount of petrol in liters he will require in order to
cross the desert? Is there a limit to the width of the desert he can cross?
How will your answer change if he has to return to the original spot?
Assume that there are no evaporation losses.
12.A hostess at her 20th wedding anniversary tells everyone "I normally ask
guests to guess the age of my three children given the sum and product
of their ages. Since Twister got it wrong tonight and Bulb got it wrong 2
years ago, I'll let you off the hook...."
You are a puzzle god and you immediately stop her saying "Their ages
are...."
Complete your statement.
But if you are not a puzzle god, you have a clue: One of their ages is 6.
13.Given that x is not an integer, find x to complete the following sequence:
35, 45, 60, x, 120, 180, 280, 450, 744
14.In a school of witchcraft and wizardry on a different planet, years which
can be written in the form y = (p^2)*q are identified as special years,
where p and q are primes. The first few of these are 12, 18 and 20.
A student is called an amateur until he reaches the first special year which
is followed by another special year (consecutive). Then he is called a
master until reaching a special year which is followed by 2 consecutive
special years when he is called a wizard and so on...He finally dies when
he cannot get to the next stage i.e. when there
exists no such special year which is followed by n-1 consecutive special
years.
When will a student in this school become a master?
When will he become a wizard?
When will he die? I.e. what is the value of n?
*Count all the years from the time of joining.
the sixty) and exactly 22 second marks ahead of the hour hand. What is
the time?
2. Nowadays as the security threat is rising, number locks are becoming
common.
Say you have a number lock having number keys from 1 to 5. You are
allowed to press either single keys or a pair of number keys simultaneously.
Also you cannot press 3 keys simultaneously or repeat a key which was
pressed previously. The order in which the keys were pressed matters but
when a pair is pressed simultaneously, there is no order between them i.e.
[(12)] is the same as [(21)].
Let’s call a key combination satisfying all these conditions as legal
combinations.
Find the number of such legal combinations.
3. You are given some matches, a thread and a pair of scissors. The thread
burns irregularly and takes 1 hour to burn from one end to the other. It has
a symmetry property that the burn rate at a distance x from the left end is
same as the burn rate at a distance x from the right end. What is the
minimum time interval you can measure accurately using the above?
Explain the method.
4. There are 26 stones having weights between 1kg and 26kg, not
necessarily distinct. All the weights are whole nos. All you have is a pan
balance. What is the minimum no. of known weights (whole numbered)
required to find the weight of each of the stones and what are they?
*Conventional methods might not always be the best ones
5.If 1 ----> 3
2 ----> 3
3 ----> 5
4 ---->4
5 ----> 4
6 ----> 3
7 ----> 5
8 ----> 5
9 ----> 4
10 ----> A . Find A.
Divide a regular hexagon into B (= A^2) pieces of two types (By types, we
mean two sets of geometric figures. Eg, a set of x congruent triangles and
a set of y congruent rectangles, where B=x+y) so that they can be
rearranged to form a single equilateral triangle.
Find x, y and the shape of the geometric figures.
(Describe in words, the division of the hexagon and formation of the
equilateral triangle)
6.You and 2 other people have numbers written on your foreheads. You are
all told that the numbers on your foreheads are prime and that they form
a triangle with a prime perimeter. You see 5 and 7 on the other 2 people.
All three of you claim you do not know the number on your forehead,
starting from you and now again it is your turn. Can you guess the number
on your forehead? Justify your answer.
7.A deck of cards has: 9 aces of spades, 8 deuces of spades, 7 threes… 2
eights and 1 nine of spade: 45 cards in total. The deck is shuffled and a
card is drawn. You should guess it by asking yes-no questions.
How can you minimize the number of questions that you will probably
have to ask? How will your answer differ
- If the deck is replaced by numbers one to one million?
- If the person who answers is permitted to lie twice?
8.Generally a ray of light can reflect many times between 2 ordinary line
mirrors. Now we introduce the condition that on each line mirror there is
only one point of reflection i.e. any ray can get reflected only at this
particular point on that mirror. Now let us call such mirrors as point mirrors.
But the laws of reflection are still dependent on the orientation of the line.
We find a maximum of 3 reflections for 2 mirrors. What is the maximum no.
of reflections for (a) 4 mirrors (b) 5 mirrors.
9.The Good, The Bad and The Ugly get into a pistol duel under unusual terms. They
draw lots and determine the order in which they start firing (who first, who second
and who third). They also decide to use the same type of pistol and bullets. Then,
they take up their positions at the corners of an equilateral triangle. They come to an
agreement that each of them will fire single shots, in turn, and continue in the same
cyclic order until two of them are dead. At his turn, the one who is firing may aim
wherever he pleases. It is also well known that The Bad always hits his target, The
Ugly hits his target three out of four turns and The Good manages only one out of
two. Assume that all of them adopt the best strategy in the duel and no one is killed
by an arbitrary shot not intended for him.
Who has the best chance to survive?
What are the exact survival probabilities of the three men?
How will your answer differ if the triangle is not equilateral and, in turns, they start
shooting bullets at regular intervals of time? Explain.
10.Gandalf and the Fellowship, finding their way through the Mines of Moria
reach a spot where they find too many paths branching out. Some
branches lead out of the Mines safely while others do not. No one knows
beforehand which branches are safe and which are not. They are
suddenly confronted by a Balrog. Panic settles in and Gandalf and the
Fellowship are separated. Both of them randomly select a distinct branch
from the set of pathways and pursue it. It is an even-money bet that both
Gandalf and the Fellowship have chosen safe pathways.
What may be the possible number of total safe pathways?
11.T-Bag is left stranded in a desolate desert area in Panama with just a
scooter and a broken hand. He discovers that there is an unlimited supply
of petrol at that particular place. He has to traverse a distance of 1000
miles and knows that there is no other petrol source on the way. His
scooter can carry petrol to go 500 miles (say L liters) and he can build his
own refueling stations at any spot on the way.
What is the minimum amount of petrol in liters he will require in order to
cross the desert? Is there a limit to the width of the desert he can cross?
How will your answer change if he has to return to the original spot?
Assume that there are no evaporation losses.
12.A hostess at her 20th wedding anniversary tells everyone "I normally ask
guests to guess the age of my three children given the sum and product
of their ages. Since Twister got it wrong tonight and Bulb got it wrong 2
years ago, I'll let you off the hook...."
You are a puzzle god and you immediately stop her saying "Their ages
are...."
Complete your statement.
But if you are not a puzzle god, you have a clue: One of their ages is 6.
13.Given that x is not an integer, find x to complete the following sequence:
35, 45, 60, x, 120, 180, 280, 450, 744
14.In a school of witchcraft and wizardry on a different planet, years which
can be written in the form y = (p^2)*q are identified as special years,
where p and q are primes. The first few of these are 12, 18 and 20.
A student is called an amateur until he reaches the first special year which
is followed by another special year (consecutive). Then he is called a
master until reaching a special year which is followed by 2 consecutive
special years when he is called a wizard and so on...He finally dies when
he cannot get to the next stage i.e. when there
exists no such special year which is followed by n-1 consecutive special
years.
When will a student in this school become a master?
When will he become a wizard?
When will he die? I.e. what is the value of n?
*Count all the years from the time of joining.
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