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Puzzle Challenge in SAP
hansen_chen
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on 2009 Jun 09 12:55 AM
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- SAP Community
Welcome to the new forum "Puzzle Challenge in SAP"
/community [original link is broken]
And have fun with puzzles.
hansen_chen
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I designed a lot of puzzles several years ago, as AI is booming, my friends suggest me to post my puzzles, so that people may get inspired with them. Actually my puzzles are not related to AI, anyway, they are related to mathematics, and mathematics is the foundation of AI. My puzzles encourage innovative thinking, which may benefit not only AI but also other high-tech areas.
In my puzzles, the symbol ★ is used to measure the difficulty of a puzzle. A puzzle with more ★ means more difficult. Anyway, a good puzzle is not necessary to be very difficult. Some puzzles with less ★ are good as long as they inspire innovative thinking.
1 stick and 5 poises ★★★★★★★★★
You have a straight stick in same thickness from top to end, and 5 poises each weighs 1 KG. If you hang 2 poises at the 2 ends of the stick and use your finger to support the stick, you can find a ½ position when the stick balances. You can mark the position. But it is not that easy to find a 1/3 position, because the stick itself has weight. Can you check a thing to verify whether it weighs:
(1) 16 KG
(2) 1/12 KG
(3) 1/30 KG
(4) 1/35 KG
(5) 2^(1/2) KG
(6) 2^(1/2)+3^(1/3) KG
(Note: don't break the stick, don't use anything as a ruler.)
----Designed in 2008
3-way puzzle ★★★★★★★
You are at an intersection, and there are 3 ways, 2 ways lead to death, 1 way leads to life. Fortunately, there is a god at the intersection. If he likes you, he speaks truly, otherwise he speaks falsely. You can ask only one yes-no question. How you find out which way leads to life? Be noted, if your question can not be answered in yes or no, he will keep silence.
----Designed in 2008
Mice and cakes ★★★★★★
There are 5 mice and 5 cakes, it takes exact 60 minutes for a mouse to eat a cake. How to measure a time period of 30 minutes? Then how about 10 minutes, 9.5 minutes? Is it possible to measure a period which is less than 10 seconds (not including 0 second)?
----Designed in 2008
Locks and chains ★★★★★★★
There are 2 rings on door and wall, if you put a chain through the rings and use a lock to lock the two ends of the chain, then the door is locked. One key can unlock only one lock. Now you have enough chains.
(1) how to lock the door with 3 locks, and all 3 keys are necessary to unlock the door;
(2) how to lock the door with 3 locks, and any 1 key is necessary and sufficient to unlock the door;
(3) how to lock the door with 3 locks, and any 2 keys are necessary and sufficient to unlock the door;
(4) how to lock the door with 5 locks, and any 3 keys are necessary and sufficient to unlock the door;
----Designed in 2008
(5) how to lock the door with 5 locks, and any 3 keys are necessary and sufficient to unlock the door. But when locking the door, there are 2 locks are already locked, each one locks a chain, the two chains are separate;
(6) how to lock the door with 5 locks, and any 3 keys are necessary and sufficient to unlock the door. But when locking the door, there are 2 locks are already locked, each one locks a chain, the two chains are connected;
(7) how to lock the door with 5 locks, and any 3 keys are necessary and sufficient to unlock the door. But when locking the door, there are 2 locks are already locked, one locks two ends of a chain, the other locks the 1/3 position to the 2/3 position on the same chain.,
----Designed in 2009
There are 12 people including 2 killers, every night one innocent guy is killed, and the following day, the people will vote the suspect. Everyone has to vote on 2 people, should not vote on himself, killer refuses to vote on killer. The guy who gets the most votes would be executed, if more than one guys get the same most votes, they are executed as well. If they can figure out a real killer from the voting, then don't have to execute the suspect who has the most votes. When a real killer is executed, his identity will be revealed. The procedure repeats everyday. Can you advise a voting solution to find out at least one killer after only 3 people died?
(Note: if you ask A vote B, but A refuses, then both A and B are killers. And one of them is already killed before the first voting, only 11 people vote on the first day.)
----Designed in 2008
This is a continuation of the first Killer puzzle. There are 151 people including 2 killers, when a guy is killed, he can identify the 2 killers, and stick out fingers or not stick out any finger on his right hand to give clue to other people(6 types of gesture). The other conditions are the same as the first killer puzzle. Can you advise a gesture and voting solution to find out at least one killer after only 3 people died?
Soon after I published this puzzle, a guy whose name is Zhuohua Wang found an optimal solution which works in 212 people scenario. The 2 solutions are totally different and are both very interesting. Can you find both of them?
----Designed in 2008
You fall into a cave and you don’t know it is day or night at the moment. You know there are 4 spirits in the cave, they are:
Spirit A speaks truly during the day and night;
Spirit B speaks falsely during the day and night;
Spirit C speaks truly during the day and speaks falsely during the night;
Spirit D speaks falsely during the day and speaks truly during the night;
When you ask questions, the spirits answer only “day” or ”night”. If the answer is not day or night, they answer randomly. Now you meet one spirit, can you identify it with two questions?
----Designed in 2009
There are 12 mice, only one of them has a different speed to eat cake. How many cakes do you need to find out the special mouse? How about 5 cakes? What if only 4 cakes?
(Note: when you let mouse A eat one cake, B eat another, if A finishes firstly, than A is faster than B.)
----Designed in 2008
Three vases would be sold one by one in an auction, each of them is worth of 2 million dollars, but 2 of them together will be worth of 8M, if someone has got 3 of them, they would be worth of 18M. There are 3 buyers, A, B, C. They have 16M, 18M, 20M respectively. And they must bid in the order A-B-C-A-B-C... The bid must be integer times of million. They are very smart, and they would rather lose money as long as the loss is less than the loss of another. What would be the auction result?
----Designed in 2008
A new version:
Three vases would be sold one by one in an auction, each of them is worth of 2 million dollars, but 2 of them together will be worth of 8M, if someone has got 3 of them, they would be worth of 18M. There are 3 buyers, A, B, C. They have 14M, 18M, 22M respectively. And they must bid in the order A-B-C-A-B-C... The bid must be integer times of million. They are very smart, and they would rather lose money as long as the loss is less than the loss of another, or as long as the loss is less than the possible profit might be got by another. What would be the auction result?
Three mugs have different capacity specification 3,4,5 liter, but one of them is a little bit different from its specification. Now you have enough water, how to find out the special one?
----Designed in 2008
The distance from A to B is 1000 meter. There are 5 people, their walk speed is 1m/s, 2m/s, 3m/s, 4m/s, 5m/s respectively. And they also have a car of 10m/s speed which can hold 3 people. Do you know how to make all of them move from A to B as quick as possible?
----Designed in 2008
There are 103 wires connecting two rooms, you can see 103 wire ends in each room, you are allowed to enter each room once with a multimeter, at least how many resistors(100ohm) do you need to identify the corresponding ends of each wire? What if you have 2 kinds of resistors(100ohm and 200ohm)?
----Designed in 2009
There are 9 wine cellars located side by side in a street, a bum is hiding in one of them. Everyday he would drink one bottle of wine and leave the empty bottle on the ground. Every night, he will move to an adjacent cellar. From the day he begins to hide, the police begin to search, every day they will search one cellar. How many days are necessary and sufficient to find the bum?
----Designed in 2008
If you can solve this puzzle, try to consider an extended one: ★★★★★★★★
There are 999 wine cellars located side by side in a street, a bum is hiding in one of them. Every day he would drink one bottle of wine and leave the empty bottle on the ground. Every night, he will move to an adjacent cellar. From the day he begins to hide, the police begin to search, every day they will search one cellar.
1. how to find the bum in less than 1020 days?
2. how to find the bum in less than 999 days?
(The extended one is not as time-consuming as imagined. And the strategy is totally different from the 9-cellar one.)
Difficult deal on vegetable ★★★★★★
Carrot $1.6 per pound, 3 carrots weigh 1 pound.
Eggplant $0.59 per pound, 3 eggplants weigh 2 pounds.
Pumpkin $1.21 per pound, 1 pumpkin weighs 5 pounds.
How to buy exact 100 pounds of exact 100 vegetables, with exact $100? (There is no tax. This is a formal store, you cannot ask for discount. Please don't cut vegetable into pieces.)
----Designed in 2008
If 1 Liter of alcohol plus 1 Liter of water makes 2 Liter of 50% wine. You have a 3 Liter jar, a 5 Liter jar, a less than 8 Liter jar, and enough water and alcohol. How to make 7 Liter of 16% wine?
----Designed in 2008
There are 10 wolves, there can survive 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 days respectively without eating anything. Now everything is gone except themselves. A wolf has to eat a whole alive wolf for a meal. They do not eat dead wolf. They don’t share food. Suppose the day before they had a meal, how long will the group of wolves survive?
----Designed in 2008
There are 5 rooms, from No.1 to No.5. A burglar is hiding in one of them. Every night, he will move to a different room, if today’s room number is X, then his new room number would be X+2 or X×2 (If it is greater than 5, then deduct 5). Everyday the police will search one room. Suppose they know the rules of the burglar, how many days are necessary and sufficient to find the burglar?
----Designed in 2009
This is an extension of the 3-way puzzle.
You are at an intersection, and there are 3 ways, 2 ways lead to death, 1 way leads to life. Fortunately, there is a dumb at the intersection. He raises right or left hand to express Yes or No, but you don't know which hand means which. If he likes you, he expresses truly, otherwise he expresses falsely. You can ask only one yes-no question. How you find out which way leads to life? Be noted, if your question can not be answered in yes or no, he will not raise hand.
----Designed in 2009
This is a variation of 2-way puzzle.
You are at an intersection, and there are 2 ways, 1 way leads to death, 1 way leads to life. There are three brothers A,B,C at the intersection. Each of them can make a correct guess on what others are going to say, but only one guess. A speaks Do and Ri, B speaks Mi and Fi, C speaks So and La to express Yes and No, but you don’t know which means which, and they don’t know others’ meaning either.
Only A knows which way leads to death or life, but he speaks Do and Ri randomly.
Only B knows whether A answers truly or falsely, but he speaks Mi and Fa randomly.
Only C knows whether B answers truly or falsely, but he speaks truly if he likes you, falsely if he does not.
You can ask only one yes-no question to one of them, and the question must have definite answer. How you find out which way leads to life?
revised version
You are at an intersection, and there are 2 ways, 1 way leads to death, 1 way leads to life. There are three brothers A,B,C at the intersection. Each of them can make a correct guess on what others are going to say, but only one guess. A speaks Do and Ri, B speaks Mi and Fi, C speaks So and La to express Yes and No, but you don’t know which means which, and they don’t know others’ meaning either.
Only A knows which way leads to death or life, but he speaks Do and Ri randomly.
Only B knows whether A answers truly or falsely, but he speaks truly or falsely in a random manner.
Only C knows whether B answers truly or falsely, but he speaks truly if he likes you, falsely if he does not.
You can ask only one yes-no question to one of them, and the question must have definite answer. How you find out which way leads to life?
extension
You are at an intersection, and there are 2 ways, 1 way leads to death, 1 way leads to life. There is a god, but he speaks truly or falsely in a random manner. You can ask only one yes-no question, and the question must have definite answer. How you find out which way leads to life?
----Designed in 2009
A guy changes socks in no more than 2 days(i.e. every morning he has to put on socks which have not been worn or has been worn for only 1 day after being washed), changes pants in no more than 3 days. He does laundry on Saturday morning, the stuff will be dry on Monday morning. Suppose he has to wear socks and pants every day, how many pair of socks and how many pair of pants at least does he need?
----Designed in 2009
Three trees make an equilateral triangle ABC. There are three mice a, b, c. They began to move simultaneously at the same speed, a from A to B, b from B to C, c from C to A, not necessarily via straight routes. Each one moved closer to its individual target by each step. And eventually everyone reached its target at same time. During the process, a and b met twice, b and c met twice, c and a met twice. Is it possible?
----Designed in 2009
Extension:
Is it possible that all three mice met twice?
You have two pieces of square paper, fold them along the midline, glue them at the midlines and make a birthday card. Now use scissors, how to cut it into 3 loops and make sure each loop connects all other loops? Furthermore, how to cut it into 5 loops and each loop connects all other loops?
----Designed in 2009
A careless cook has cut 5 fingers off his left hand, today he cut another finger off his left hand, but he was not a six-fingered man, is it possible?
----Designed in 2009
When five guys were walking, some birds flew over and left **bleep** on their heads. Everyone could see **bleep** on other people’s heads, but could not see that on his own head. They entered a coffee shop, the seller said: “The count of **bleep** on each of you is between 1 and 9, and everyone has a unique count. You guys must not communicate. If anyone can make a correct guess of his own count, I will provide free coffee to all of you.” If the five guys could imagine the situation and could have a discussion beforehand, what strategy they may implement?
Enhanced variation: ★★★★★★★★
Six people with hats on their heads. Everyone can see other people's hats, but cannot see his own hat. The hats have 3 colors, red, blue, yellow. There is a number on each hat, the number is between 1 and 9, and all the numbers are different. They cannot communicate, everyone can make 2 guess. They can discuss beforehand, what strategy can they implement in order to make at least one guy to give at least one correct guess on both of his own color and number?
Enhanced variation II: ★★★★★★★★★
N people with hats on their heads. Everyone can see other people's hats, but cannot see his own hat. There are 3 numbers in 3 colors (red, blue, yellow) on each hat. (for example, a hat has numbers: red 2, blue 3, yellow 2) The numbers are between 1 and 3. They cannot communicate, everyone makes a guess on his own 3 numbers. There is a solution to make at least one guy to guess at least 2 numbers correctly. What the smallest N can be (>0)?
Enhanced variation III ★★★★★★★★★★
N people with hats on their heads. Everyone can see other people's hats, but cannot see his own hat. There are 3 numbers in 3 colors (red, blue, yellow) on each hat. (for example, a hat has numbers: red 2, blue 3, yellow 2) The numbers are between 1 and 8. For each color, all the hats have different numbers. They cannot communicate, everyone makes a guess on his own 3 numbers. There is a solution to make at least one guy to guess at least 2 numbers correctly. What the smallest N can be (>0)?
----Designed in 2009
When seven guys were walking, some birds flew over and left **bleep** on their heads. Everyone can see **bleep** on other people’s heads, but cannot see that on his own head. They entered a coffee shop, the seller said: “The count of **bleep** on each of you is between 1 and 9, and there are two pairs among you, in each pair the counts of **bleep** are same, (e.g. seven guys A,B,C,D,E,F,G, the count of **bleep** on A is same as that on B, the count on C is same as that on F), and the others have different counts. You guys must not communicate. If anyone can make a correct guess of his own count, I will provide free coffee to all of you.” If the seven guys could imagine the situation and could have a discussion beforehand, what strategy they may implement?
Enhanced variation:
When seven guys were walking, some birds flew over and left **bleep** on their heads. Everyone can see **bleep** on other people’s heads, but cannot see that on his own head. They entered a coffee shop, the seller said: “The count of **bleep** on each of you is between 1 and 10, and there are two pairs among you, in each pair the counts of **bleep** are same, (e.g. seven guys A,B,C,D,E,F,G, the count of **bleep** on A is same as that on B, the count on C is same as that on F), and the others have different counts. You guys must not communicate. If anyone can make a correct guess of his own count, I will provide free coffee to all of you.” If the seven guys could imagine the situation and could have a discussion beforehand, what strategy they may implement?
----Designed in 2009
Christmas light bulbs ★★★★★★★★
There are N Christmas light bulbs. Only one of them has a different resistance, and you don't know the exact resistance value. Given a 12V battery with unknown internal resistance, sufficient wires, and a perfect voltmeter(unlimited resistance), there is a way to find out the odd bulb by using the voltmeter 4 times. What the greatest N can be?
Revised version:
There are N Christmas light bulbs. Only one of them has a different resistance, and you don't know the exact resistance value. Given a 12V battery with unknown internal resistance, sufficient wires, and a perfect voltmeter(unlimited resistance), there is a way to find out the odd bulb by using the voltmeter 3 times. What the greatest N can be?
Variation:
There are N resistors. Only one of them has a different resistance. Given a 12V battery with unknown internal resistance, sufficient wires, and a special Light-emitting diode(there are 2 pins, red and blue, it emits red light when current enters from red pin, emits blue light when current enters from blue pin, same brightness when the currents' volumes are the same), you can compare the brightness among different tests. There is a way to find out the odd resistor by using the diode 3 times. What the greatest N can be?
----Designed in 2009
2010 is a game year(Olympic winter game in Vancouver), let's have some fun.
This is a special matrix, you may start from any element, move vertically or horizontally to an adjacent element. The number in each element denotes the times you are required to move in. 0 means you are not allowed to move in. N means you can move in any times you want including 0.
For example, if the matrix is like:
1 2 1
1 1 1
1 0 1
Then you can move from the left corner, and move in this way: U-U-R-R-L-D-R-D
OK, let's try the following two matrix mazes:
1 2 N 1
1 3 3 1
1 2 3 1
1 1 1 0
０１１１１１０
０１１１１２１
０１１Ｎ２１１
０１０１２１１
１１１１２１１
１２２２１０１
１２１１１１１
And we can also create more elements to the maze.
P means you can jump to any position
B means you must begin from it, and no longer move in.
E means you must end at it, and move in once.
> < v ^ means you will jump at the arrow direction to next direction symbol.
Try this:
B 1 P 1
3 2 1 2
> N < 2
2 2 1 E
----Designed in 2009
Prerequisite knowledge: when transfer data through network, error may happen. Suppose we want to transfer 1001, and the error would happen on only one bit, we may add some parity-check code like this:
---Co1-Co2-XOR
Ro1--1--0--1
Ro2--0--1--1
XOR--1--1
Then you transfer 10101111 instead of 1001, and the person who receives the data would be able to figure out the original data.
The puzzle is: you want to transfer 1000 bits data over the network, and the error may happen on only one segment of the data, (e.g. from bit 11 to bit 233), and all the 1 in that segment will turn into 0, 0 will turn into 1. You may add some check code to the data, how many bits at least are enough for you to make a secure transfer?
----Designed in 2009
Tom walked to east 1000 meters, to north 1000 meters, to south 1000 meters, and reached the position where he started to walk. Where is the position on earth?
----Designed in 2008
There are 4 switches on a wall side by side, each connected with a long rope hanging. You can only see the lower end of each rope. Now the 4 ropes might cross each other, for any TWO of them, if they cross each other, they only cross ONCE. You can pull any rope, if it doesn’t cross other ropes you will turn on the connected switch, and a light will be turned on. And you can switch the position of the ends of ropes to make them don’t cross each other. How many tries of pulling at least do you need to turn on all the switches?
----Designed in 2010
N computers are connected in a ring network. Message delivery only takes place between adjacent computers. That is: when #1 computer needs to send message to #4 computer, it has to send to #2, and then #2 sends to #3, and at last #3 sends to #4. And #1 is adjacent to #N. To improve the performance, you can add another ring network to connect all the computers in a different sequence, for example, #1 to #8 to #4 to #15 and so on. Between any given 2 computers, the message can be successfully transferred in less than 4 deliveries. How large the N can be? What if there are 3 ring networks?
----Designed in 2009
A frog can jump 1 foot high, and spend 1 second, assuming its speed is the same during the jump. When a frog is at the top of a jump, another one (and only one) can step on it and make a new jump. Now there are 16 frogs, how high can a frog reach?
----Designed in 2010
People A,B,C,D, each is at each edge of a square, the square side is 100 meter. A moves to B, B moves to C, C moves to D, D moves to A at speed 1m/s. Simultaneously a bird flies from A to B, then to C, then to D, then to A and so on. The bird meets D for the first time at the 30 second, when will it meet D for the third time?
----Designed in 2009
This is a variation of the 4-dog puzzle, it requires a little bit calculation but not too much.
There are 12 mice in same weight and 6 cakes. And one of them is special, that is: either one mouse has a different speed on eating or one cake weighs differently. Now you put 6 mice and 3 cakes on each side of a balance scale. If you take anyone off, you are not allowed to put it in, not change sides. Mice can eat cakes anywhere. Every cake need to remain a part at last. Can you find out the special one?
----Designed in 2009
Whiteboard and projection screen ★★★
There is a whiteboard and a projection screen in the classroom, students need to watch both board and screen. However if you turn on the light, the projected image on the screen is unclear; if you turn off the light, the content on the board is unclear. How to solve the problem?
----Designed in 2006
The engine rotates one round per second. You can use sufficient wheels at the diameter of any integer meters. Only the edge of wheels is allowed to touch ground. You can weld them with steel pipes to make a car. Only edge is allowed to deliver motion from wheel to wheel. The car goes straight. Is it possible that the car’s speed is exact 3 meters per second?
----Designed in 2010
There are two locks on a door, each lock contains 3 wheels, each wheel contains 10 number(from 0 to 9), but the sequence on each wheel might differ from others(for example, one wheel is 1,2,3,4.., anthor is 3,6,0,2...). When you try to open the door, if the numbers on both locks are same, or the number on any one lock is the same as the other at the last try, then the door opens. Unfortunately, it is in the dark, you cannot see the number. How many tries at least is sufficient to open the door?
----Designed in 2010
A cruise finds a submarine below, and can detect its depth. The sea is 1000 meters deep. In each minute, the submarine can move up or down 100 meters, or stay at its position, so there are 10 positions altogether, from 100m to 1000m. The cruise can drop depth charges, which are bombs explode at the pre-set depth under water. (for example, if you set the depth to 100m, then it explodes at the 100m position.) The depth charges move down 100m per minute. The explosion at the same position of the submarine will sink the submarine, but the explosion doesn't affect other depth charges. No more than two depth charges are allowed to explode at the same time. How many depth charges are enough to sink the submarine surely?
----Designed in 2010
Seven people stand in circle ★★★
ABCDEFG seven people stand in a circle, every one holds hands with people who stand next to his adjecent people. We have
Hands between BD are above hands between CE.
Hands between CE are above hands between DF.
Hands between DF are above hands between EG.
Hands between EG are above hands between AF.
Hands between AF are above hands between GB.
And A's hand hasn't hold C's hand yet, how do they hold hands in order to achieve this: without releasing any hand, these people can change position and stand in a bigger circle and everyone hold hands with adjecent people.
----Designed in 2009
There are N balls on a flat surface, you can watch from side, you can choose any angle, what you can see is shadows of the balls on the side. How many times at least do you need to watch so you are are sure to figure out the N?
There are N balls in 3D space, you can watch at any angle, what you can see is shadows of the balls on the side where you watch from. How many times at least do you need to watch so you are sure to figure out the N?
----Designed in 2010
There is a dark knight on a 4*4 squares chessboard. After each move of the knight, you can check N squares, what is the smallest N to be necessary to find the knight?
----Designed in 2010
Two boys don't know age of each other, one day they met grandpa and asked him about his age. Grandpa said: "The addition of digit in tens place and the digit in ones place of my age is equal to the subtraction of digit in the tens place and the digit in ones place of age of one of you." The two guys thought hard, but didn't figure it out. The second day, they came to ask grandpa again, grandpa said: "My age is equal to the multiplication of the addition and subtraction of your ages." The two guys could not figure it out. The third day, they came to grandpa, grandpa said: "My age = (age of one of you)*7 - (age of the other)*4" The two poor boys still could not figure it out, the forth day, grandpa said: "One of you, whose age I didn't refer to in the first day, exchange his age's digit in tens place with digit in ones place, then minus the addition of the digit in tens place and the digit in ones place, the result is equal to my age." Can you figure out grandpa's age?
----Designed in 2009
When a group of guys were walking, some birds flew over and left **bleep** on their heads. Everyone can see **bleep** on other guys' heads, but cannot see that on his own head. They entered a coffee shop, the seller said: “There are 3 guys among you who have same count of **bleep**, and there are a few pairs, the guys within each pair have same count, the rest have different count of **bleep**. Of course, the counts for all the pairs and previous mentioned 3 guys are all different. You guys must not communicate. If anyone can make a correct guess of his own count, I will provide free coffee to all of you.” If the guys could imagine the situation and could have a discussion before hand, they are sure to find a strategy. Do you known how many guys there are at most?
----Designed in 2010
John received a gift card on New year day, the credit is from $0 to $1000. The card can be used successfully only once, for example, if he uses it to buy something worth $100, and the credit is $500, he actually loses $400. If he buy something that the price is higher than the credit, the deal is not successful, and the bank would remove 10% of existing credit from the card. Suppose the unit is $1.How should John use the card wisely?
----Designed in 2009
Five people are smiling ★★★★★★
Five people, there is an integer on each one's head. Everyone can see other people's number but cannot see his own number, and each one can give other people a hint by choose either smiling or not. The number range is from 0 to N. And they are sure that at least one can make a correct guess on his own number. What might be the greatest N?
----Designed in 2009
Two people take turns planting trees in a 100 meters street, one tree in each turn, the tree is 4 meters wide. The one who has no place to plant wins. Who will be the winner?
----Designed in 2011
This is a variation of Nim.
There are two magic time boxes. One box makes the time in it sqrt(2) times as fast as the time out of it. The other box makes the time in it sqrt(3) times as fast as the time out of it. You have two straight sticks, each is 1 meter long, and have twoFishing, they move at same speed. (Be aware, an ant seems faster when it is in a box.) The boxes are transparent, and you can make accurate comparison on distance which ants have moved between sticks even in different boxes. How to find 1/3 meter length? How to find 1/5 meter length?
----Designed in 2010
There is no limitation on boxes’ size (you can enter a box if you want). You can mark the sticks. You are not allow to break them. You can do anything reasonable, for example: put a part of stick in one box, and put the rest of it in the other box.
On a 8*8 chess board, there is a queen. On each turn, the queen moves N steps at a fixed direction. When hitting the edge, the direction is changed to the reflected one. When hitting the corner, the direction is changed to the reversed one. And after each M turns, the direction rotates 45 degree clockwisely. You don't know the original position, direction, N and M. On each turn, you can check a single square on the chess board. Do you have a strategy to be sure to find the queen?
----Designed in 2010
100 light bulbs and 100 switches ★★★★★★★★
There are 100 light bulbs in one room corresponds to 100 switches in another room. Currently all the switches are turned off. You can only enter each room once. You are not allowed to add new wires between the rooms or use external equipment. You cannot feel the temperature of the bulbs. Can you figured out which bulb corresponds to which switch?
----Designed in 2011
Six capacitors and their specification are 1, 1/2, 1/3, 1/4, 1/5 and 1/6F respectively. And only one of them is different from its specification. Given an ideal battery, several light bulbs and sufficient wires, you need to find out the special one. Each bulb can only be lighted up once before it is destroyed. Assume that the brightness=Voltage*Capacity, that is equal to the volume of electricity in the capacitor. And you can compare the brightness.
1. At least how many bulbs do you need to be sure to find out the special capacitor?
2. What if there are 5 capacitors? and the smallest one is 1/5F.
3. What if there are 4 capacitors? and the smallest one is 1/4F.
4. What if there are 3 capacitors? and the smallest one is 1/3F.
----Designed in 2010
Poisoned Wine and special slave ★★★★★★★
There are 240 bottles of wine, one of them is poisoned, it would kill a person who drinks it in one day. Now the king has slaves to test the wine. There is a special slave who can survive after drinking the poisoned wine, but would die if he drinks the wind which doesn't contain poison. The king doesn't know which the special one is. He needs to identity the poisoned wine in one day, how many slaves at least does he need?
----Designed in 2009
12 rubber binders in same size, only one of them has a different elasticity. You can use a hook on the ceiling and a coat hanger. How many times do you need to test to find out the special rubber binder?
----Designed in 2008
Huang Yaoshi was a super kong fu master. One day he was trapped on thin ice and could not walk. There was a tree 10 meters away. He had a rope, he need to wrap the rope to the tree at least 2 rounds so as to tie the tree firmly. Hopefully he caught a mouse, and he tied an end of the rope on the mouse's tail. He had some peanuts. The mouse could smell peanuts within 1 meter and go to eat them. Huang is good at shooting peanuts to accurate position, but he need to shoot all peanuts before releasing the mouse. How many peanuts at least did he need? No need to consider the size of tree, rope, mouse and peanut.
----Designed in 2009
Direction of magnetic field ★★★★★
You have two watches, yon have to lay the watches horizontally. The watches are in a magnetic field, the magnetic direction is horizontal. The hand of watch moves faster when it is with the magnetic direction, and moves slower when it is against the magnetic direction. And it takes exact one minute to move one circle. Suppose you can see the accurate position of the hands, how to figure out the magnetic direction with the two watches?
----Designed in 2010
I just bought an antique vase at price $1000, but there is a probability to be a fake. The only way to identify the fake is to smash it. If I find it is a fake, I can get double of what I have paid back from the seller. If I don't smash it, I can sell it to another person at doubled price. Then the new buyer will play the role that I have played, and so on. Assuming everyone knows the exact value of the probability, how to decide whether to smash it or sell it?
----Designed in 2010
On an 8*8 chess board, there are 16 chessmen. There are 16 people, everyone's name is written at the bottom of a chessman. At the beginning, no one knows the layout of chessmen. Everyone is allowed to come to the chess board sequentially, and guess which chessman has his own name. After guessing, he can check all the chessmen, and he can also move a single chessman. How could they make a plan so that at least 15 people make correct guess?
----Designed in 2011
An edge on the Rubik's cube ★★★★★★
- There is a 2*2*2 Rubik's cube at the center of a table, one side faces to east. The cube is made of 8 small cubes, each small cube has 12 edges. One of the 96 edges is defined as #1. Tom and Jack can have a discussion before seeing the cube. Firstly, Tom comes to the table, he is told which edge is #1. He can pick up the cube, rotates any side, but only once, then puts it back. And then Jack comes to the table, how does he make a correct guess on what the position (relative to the table) of the edge is originally before Tom touches it?
- There is a 2*2*2 Rubik's cube at the center of a table, one side faces to east. The cube is made of 8 small cubes, each small cube has 12 edges. One of the 96 edges is defined as #1. Tom and Jack can have a discussion before seeing the cube. Firstly, Tom comes to the table, he is told which edge is #1. He can pick up the cube, rotates any side, but only once, then puts it back. Then Jack comes to the table, how does he make a correct guess on where the #1 edge is?
----Designed in 2012
There are 9 fuel rods and 9 fuses, to light up a fuel rod, you have to bind it with a fuse and ignite the fuse firstly. To ignite a fuse, you have to keep on heating it for a given period. If stop heating before it is ignited, you have to heat it again from the beginning. It takes 1,2,3,4,5,6,7,8,9 minutes to ignite the 9 fuses respectively. And the fuel rods can burn for 1,2,3,4,5,6,7,8,9 minutes respectively. One rod can only heat one fuse at a time. Now you have an igniter which can burn for 1 minute. How to light up all fuel rods? The second question is with more limitations, the 6-minutes fuse is bound with 4-minutes rod, the 4-minutes fuse is bound with 6-minutes rod, the 2-minutes fuse is bound with 8-minutes rod, the 8-minutes fuse is bound with 2-minutes rod, how to bind other fuses and rods?
----Designed in 2009
This is a board game. Two players, one holds a red pan, the other holds a blue pen. They draw points on a white paper in turn. It does not allow overlap. If any five points in same color satisfy a condition, then the one who owns the color wins. The condition is: 4 points make a rhombus, and the fifth one is its center.
----Designed in 2012
Two 400 cc glasses, the section of each glass is isosceles trapezoid. You can make marks on the glasses. You come to a pool with sufficient water. How to get exact 300 cc water?
----Designed in 2011
Genderless electrical connector ★★★★★
I ever heard of the genderless electrical connectors, but I didn’t find any article which gives a general rule of the design. So we still have chance to innovate. Suppose we are to connect two electrical equipments with cables, the connectors on equipments and cables are required to be identical. To increase the length of cable, multiple cables can be linked. There are only four pins are allowed in each connector. How to design the connector to satisfy the following requirements respectively?
- Straight through connection, pin to pin is like 1-1, 2-2, 3-3, 4-4.
- Crossover connection, like 1-4, 2-3, 3-2, 4-1.
- Half straight through half crossover, like 1-1, 2-2, 3-4, 4-3.
----Designed in 2012
Two men are walking toward each other, at the beginning the distance between them is 100 meters. Each of them is holding a gun with 3 bullets. At each integer meters of distance, each one is allowed to shoot one bullet. Each will be killed when he is hit by a single bullet. The probability of missing is Distance/100. If you are one of them, what strategy you will apply?
----Designed in 2009
Make a touch screen with 8*8 points. Each time when it is contacted by a finger, there are always 2*2 points triggered, the standard of resolution is not high and it is okay if any one of the 4 points can be determined by the CPU. Multiple points can share one wire. One point connects only one wire. At least how many wires are enough to make the touch screen?
----Designed in 2012
Four dots on a piece of paper ★★★
How to draw 4 dots on a piece of paper? So that it takes same time for an ant to move between any two dots. Suppose the ant knows the shortest route.
----Designed in 2009
There are a few points on the paper, each two points are connected with either red or blue line, and there is no cross between any two lines in same color. How many points could be there at most?
----Designed in 2012
There are two shuffling machines, A and B. When you insert a pile of cards at the order 1,2,3,4,5,6 into A, it always shuffles them into the order 4,6,3,5,1,2. When you insert a pile of cards at the order 1,2,3,4,5,6 into B, it always shuffles them into the order 3,2,4,1,5,6. Now you have a pile of cards at the order 4,2,5,3,1,6. You can shuffle them only with the two machines. How to make them into the order 1,2,3,4,5,6?
----Designed in 2010
Assuming the scent of sugar can attract an ant, and the degree of attraction is equal to Weight/Distance. The ant is always moving towards the sugar which has the greatest attraction. When the ant reaches a piece of sugar, it eats the sugar. Now there are 5 pieces of sugar, how many turns at most can be there on the ant's path?
----Designed in 2012
Tom said: Can we assume there is another earth? It is at the symmetry point in the solar system, and it is always blocked by the sun, so we have never seen it.
Mike said: Impossible. Because the earth's orbit is an oval, when one earth is moving faster when it is closer to the sun, the other earth is moving slower at the other side. So it cannot be blocked by the sun most of the time.
The question is: Does Mike make sense?
----Designed in 2008
John is to distribute one pound salt, one pound sugar and one pound flour to Jerry, Mike and himself. The proportion of price for these three kinds is 1:2:3 in his eyes, 2:3:1 in Jerry's eyes and 3:1:2 in Mike's eyes. He divides the food, and gets his own portion firstly. Then Jerry and Mike will take their own, they will calculate the value of portions based on their individual rule, and have to accept the portion if it is not less than other one’s portion. How does John divide the food so as to get the most?
----Designed in 2013
Six bottles line up on a table, two red, four blue. There is less than a half of bottle of water in each of them. No two bottles have same volume of water. Suppose you have a color blind friend, you and your friend can discuss beforehand. Firstly you come to the table. You can pick up one bottle, pour some of the water (not all) to another bottle and then put it back. Be sure that no two bottles have same height of water. Secondly your friend comes to the table and judges which two bottles are red. Note that he can tell which has more and which has less, but cannot tell how much more or less. Do you have a good solution?
----Designed in 2012
You fall into a cave and you don’t know it is day or night at the moment. You don't know it is cloudy or not. You know there are 8 spirits in the cave.
When it is not cloudy:
Spirit A speaks truly during the day and night;
Spirit B speaks falsely during the day and night;
Spirit C speaks truly during the day and speaks falsely during the night;
Spirit D speaks falsely during the day and speaks truly during the night;
Spirit E speaks falsely during the day and night;
Spirit F speaks truly during the day and night;
Spirit G speaks falsely during the day and speaks truly during the night;
Spirit H speaks truly during the day and speaks falsely during the night;
When it is cloudy:
Spirit A speaks falsely during the day and night;
Spirit B speaks truly during the day and night;
Spirit C speaks falsely during the day and speaks truly during the night;
Spirit D speaks truly during the day and speaks falsely during the night;
Spirit E speaks truly during the day and night;
Spirit F speaks falsely during the day and night;
Spirit G speaks truly during the day and speaks falsely during the night;
Spirit H speaks falsely during the day and speaks truly during the night;
When you ask questions, the spirits answer only “day” or ”night”. If the answer is not day or night, they answer randomly. Now you meet one spirit, can you identify it with three questions?
----Designed in 2010
Acrobat and spinning dishes ★★★★★
An acrobat is good at spinning dishes. Suppose there are a few dishes in a line. The distance between each two adjacent dishes is 1 m. The speed of acrobat is 2 m/s. It takes him 1 second to make a dish spin, and the dish can keep spinning only for 16 seconds. The acrobat can keep all the dishes spinning forever, how many dishes at most are there?
----Designed in 2009
A thin pole with same elasticity at any position, if you connect two ends of the pole, will it make a circle?
----Designed in 2008
Mick and Jerry each has 100 coins in pocket. Every time, each picks some of the coins to compare who has more coins in hand. The coins they have compared can't be used any more. They compare three times, is there a strategy for Mick to be able to win more times?
----Designed in 2012
There are 12 coins, only one of them weighs differently from others. Now you have a cheating balance. When two sides weigh the same, one random side moves down. When two sides weigh differently, it maintains balance or the side which weighs lighter moves down. Are you able to find out the special coin with the balance?
----Designed in 2008
I made a variation of a famous puzzle.
The original one is:
There are two identical crystal balls and you need to find out which is the maximum floor in a 100 storey building from where the balls can fall before they break. In the most efficient way, what will be the maximum number of drops required to find the right floor in any possible scenario? The balls are allowed to be broken (if required) while finding the right floor.
The variation is:
This is a competition between two people, they each has two identical crystal balls and needs to find out which is the maximum floor in a 100-storey building from where the balls can fall before they break. They test separately, the one who finds the right floor with less number of drops wins. If you are one of them, what is your strategy to win in most possible scenarios?
----Designed in 2012
100 couples and a light bulb ★★★★★★★★
This is a variation of a famous puzzle: 100 prisoners and a Light Bulb
100 couples are arrested and sent into 200 solitary cells. There's a central living room with one light bulb. No prisoner can see the light bulb or the living room from his or her own cell. Every morning, the warden picks a woman randomly and let her visit the living room. Every afternoon, the warden picks a man randomly and let him visit the living room. The prisoner can toggle the bulb in the living room. Also, the prisoner has the option of asserting that every couple have been picked on a same day at least once by now. If this assertion is false, all prisoners are shot. However, if it is indeed true, all prisoners are set free. The prisoners are allowed to get together one night in the courtyard, to discuss a plan. What plan should they agree on, so that eventually, someone will make a correct assertion?
----Designed in 2013
A spy uses a window to deliver messages. There are 3*3 pieces on the window. He can put stickers on some of the pieces to show specific information. Every time he shows only two words, regardless their sequence. Suppose each word is shown as 3*3 matrix made with stickers. For example
★_★
★_★
___
is Jack.
_★★
___
_★_
is Tom.
And he always merges the two matrixes of stickers to express the two words, like
★★★
★_★
_★_
means Jack and Tom.
The question is how many words he can use in total?
----Designed in 2012
There are 7 electrodes in different voltages, -3 volt, -2 volt, -1 volt, 0 volt, 1 volt, 2 volt, 3 volt. You can connect a bulb to any two electrodes, and compare brightness. How many times you need to try to find out the electrode which is 0 volt?
----Designed in 2010
There are two electric fans, you can adjust the rotation speed on one of them. How to make its speed the same as the other's?
----Designed in 2012
Weight which can be cut ★★★★★★★
You are to validate the weight of TWO cakes with a balance scale. The weight of cakes is A and B grams respectively, A and B are integers and both no more than X gram. Before you are told the values of A and B, you need to prepare three weights. And after you are told the values of A and B, you can cut one weight into two parts, and each part weighs the accurate integer grams which you want. Then you can use the four weights to validate the two cakes. The question is what the greatest value of X it can be, so that you can always successfully validate any value of A and B.
----Designed in 2010
There are 100 students in a class. To confirm the amount, they need to count themselves, there are different ways to count, for example, let one student counts one by one, it takes one seconds to count one student, or let more than one students to count, it takes four seconds to sum the counts from any two students. Can you make a strategy to count all students ASAP?
----Designed in 2014
Diamond covered by hats ★★★★★★★★
There are three hats on the table, make a triangle, the color is red, blue, yellow respectively. One of them covers a diamond. Three people A, B, C are to guess where the diamond is. Their favorite color is red, blue, yellow respectively. Each person doesn't know other people's favorite colors, but knows they are different from each other. Besides,
A knows the hat in B's favorite color covers the diamond;
B knows the hat at the left side of the hat in C's favorite color covers the diamond;
C knows the hat at the right side of the hat in A's favorite color covers the diamond;
A, B, C can in turn ask anyone a question, one's answer can be true or false, but if true, has to be always true, if false, has to be always false. They all are smart. Do you know who can find the diamond firstly? Be noted, each question has to be a Yes/No question with fixed answer. Other people can hear the conversation and get some clue.
----Designed in 2011
World cup fans puzzle ★★★★★★★★★
There are N groups of soccer fans, each group has 6 people representing 6 countries. Each person is asked to guess the rank of his/her own country. No one knows the ranks except an expert who made ranks for the 6 countries. One after the other, each one enters a room, speaks out the number of rank, if it is incorrect, the expert will tell him/her which country ranks that number. Everyone has 3 chances to guess, then leaves the room with no communication with other fans. If anyone in a group fails, the group fails. Fortunately all fans can get together and make a strategy beforehand. So far the puzzle is pretty much like the "Names in boxes" puzzle (http://gurmeet.net/puzzles/100-prisoners-and-100-boxes/). Anyway, the question is different. What is the least N can be so that they can guarantee at least one group would win?
----Designed in 2010
There is a cake. Jack finds it circle, Tom finds it rectangle, Jerry finds it triangle. What the real shape is it?
----Designed in 2014
Three doors ★★★★★★★
There are three doors #1,#2 and #3, one life door and two death doors. A guard knows which the life door is. He never answers your question but he will say "1","2" or "3" after you have said two statements. He is one kind of below.
1: When both statements are right, he says 1; when only one is right, he says 2; when both are wrong, he says 3.
2: When both statements are right, he says 2; when only one is right, he says 3; when both are wrong, he says 1.
3: When both statements are right, he says 3; when only one is right, he says 1; when both are wrong, he says 2.
4: When both statements are right, he says 1; when only one is right, he says 3; when both are wrong, he says 2.
5: When both statements are right, he says 2; when only one is right, he says 1; when both are wrong, he says 3.
6: When both statements are right, he says 3; when only one is right, he says 2; when both are wrong, he says 1.
However you don't know what kind of person the guard is. How to say two statements and find out the life door based on the guard's comment? Note, you are not allowed to use "And" or "Or" logic on your statements.
----Designed in 2014
There are four doors #1,#2,#3,#4, one life door and three death doors. A guard knows which the life door is. He never answers your question but he will say "1","2","3" or "4" after you have said two statements. You knows the numbers are corresponding to four states: both statements are right, only the first one is right, only the second one is right, both are wrong. But you don't know which number is corresponding to which state. How to say two statements and find out the life door based on the guard's comment? Note, you are not allowed to use "And" or "Or" logic on your statements.
----Designed in 2014
Seven cards ★★★★★★★★★
Tom is given seven cards with different number on each one, the range of number is from 1 to 76, he shows five cards to Jack one by one, then Jack knows the numbers on the rest two cards. Suppose they can discuss before Tom gets the cards, what strategy they may apply?
----Designed in 2014
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