Looking for genius!!! Don't give up the chance!!!

[hansen_chen]

I am going to design some innovative features in spare time on Web Intelligence Report. As the success relies on team work, I hope genius to take part in it. I designed some small puzzles at below. You are welcome to join if you can solve anyone of them.

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Puzzle: A special mouse

There are 12 mice, only one of them has a different speed to eat cake. Can you find out the special mouse?

1. With 5 cakes, to eat 3 cakes at the beginning;

2. With 5 cakes, but not to eat 3 cakes at the beginning;

3. With 4 cakes.

(Note: The cakes have same size, you can order the mice to eat or to stop, the difference of their speed is less than 1%, but you can clearly observe which cake is gone firstly. You may also split a cake in half or even quarter, the parts may be similar in size, but perhaps not exactly the same.)

Puzzle: 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 you 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 validate the weight of a thing which is specified as:

(1) 16 KG

(2) 1/12 KG

(3) 1/30 KG

(4) 1/35 KG

(5) 2^(1/2) KG

(6) 1/7^(1/3) KG

(7) 2^(1/2)+3(1/3) KG

(Note: don't break the stick, don't use anything as a ruler.)

Puzzle: Killer

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 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 is already killed before the first voting.)

Puzzle: Killer II

There are 212 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?

(Note: there is also a totally different solution for 151 people scenario, both solutions are very hard to imagine.)

A bum in wine cellars

There are 9 wine cellars located side by side in a street, a bum is hiding in one of of them. Everyday he would drink one bottle of wine and leave the empty bottle on the ground. Everynight, he will move to an adjacent cellar. From the day he begins to hide, the police begin to search, everyday they will search one cellar. At least how many days are enough to find the bum?

Auction

3 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 have got 3 of them, they would be worth of 18M. They are 3 buyers, A, B, C. They have 16M, 18M, 20M respectively. And they must bid in the order A-B-C. The bid must be integer times of million. They are very clever, and they would rather lose money as long as the lose is less than the possible profit won by others. What would be the auction result?

5 line segments

In a 3 dimension space, there are 5 line segments not connecting to each other. The distance means the distance between closest points on the line segments. How to make the distance to be same between any two of them? Think about 6 line segments if you finish the first question.

The 2 missing characters

We know there are 26 characters in English. Now there are 8 different characters, the first person can read the first 7 of them, the second person can read the last 7 of them. The first person tells you 3 characters, and tells the second person 1 character, then the second person tells you 3 characters. Can you figure out what are the 2 charaters un-told? Of course you three may discuss a solution beforehand.

3 mugs

Three mugs have different capacity specification 3,4,5 liter, but one of them is a little bit different from what is specified. Now you have enough water, how to find out the one? What if the capacity is 5,7,11 liter?

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)?

By Hansen Chen

SAP Business Objects

[Former Member]

Measure a period less than 10 seconds:

1. Two mice eat cake1, one mouse eats cake 2, one mouse eats cake3, one mouse eats cake4. => Cake2, cake3 and cake4 each has 30 minutes left

2. Three mice eat cake2, one mouse eats cake5 => Cake3 and cake4 each has 30 minutes left; cake5 has 50 minutes left

3. Two mice eat cake5, one mouse eats cake3, one mouse eats cake4 => Cake3 and cake4 each has 5 minutes left.

4. Two mice eat cake3, three mice eat cake4 => Cake3 has 5/6 minute left

5. Five mice eat cake3 => The period of time between they start and before they finish (not including the point when the cake is completely gone) is less than 10 seconds.

[Former Member]

Hi Hansen,

I can make the mice measur 9.5 minutes.

Measure 9.5 minutes:

1. Three mice eat the 1st cake and two mice eat the 2nd cake. By the time the 1st cake is finished (20 minutes), there is 20-minute worth of 2nd cake left;

2. Two mice eat the leftover of the 2nd cake, one mouse eates the 3rd cake and one mouse easts the 5th cake. By the time the 2nd cake is gone (20/2 = 10 minutes), there is 50-minute worth of 3rd cake left and 50-minut worth of 5th cake left;

3. One mouse eats the leftover of the 3rd cake and one mouse eats the 4th cake. By the time the 3rd cake is finished (50 minuts), there is 10-minute worth of the 4th cake left;

4 Four mice eate the leftover of the 4th cake and 1 mouse eates the lefterover of the 5th cake. By the time the 4th cake is finished (10/4 = 2.5 minutes), there is (50 -2.5= 47.5) minute worth of the 5th cake left. It takes 9.5 seconds for five mice to finish this remaining of the 5th cake.  

I'll make them measure a time of less than 10 seconds later.

[Former Member]

Just found these interesting puzzles. Try to solve the first one.

Solution of the speical mouse puzzle:

Suppose the 12 mices are labled with the number 1 .. 12.

A. 5 cakes, to eat 3 at the beginning.

Separate the 12 mice into 3 groups evenly, ask them to eat A, B and C simultaneously. Stop all mice once there is a cake finished.

A1. A being eaten by 1, 2, 3 and 4 is finished firstly when B and C are not. Ask 1 and 2 to eat the rest of B, 3 and 4 to eat the rest of C. Suppose B is finished firstly, then ask 1 and 2 to eat D and E simultaneously and the one finishes firstly is the quick one.

A2. A and B are finished simultaneously when C being eaten by 1,2,3 and 4 is not yet. Ask 1, 2, 3 and 5 to eat D, 6,7,8 and 9 to eat E. If D and E are finished simultaneously, 4 is the slow one. Otherwise, stop all mice once E is finished. Ask 1 and 2 to eat the rest of C and D, if they finish simultaneously, then 3 is the slow one, otherwise pick the slow one in 1 and 2.

B. 5 cakes, not to eat 3 at the beginning.

Separate the 12 mice into 3 groups evenly. Ask 1, 2, 3 and 4 to eat A, 5, 6, 7, 8 to eat B, simultaneously, stop all mice once there is a cake finished. Suppose A is finished firstly. Ask 1, 2, 3 and 9 to eat C, 5, 6, 7 and 10 to eat B, 4, 8, 11 and 12 to eat C, simultaneously, and stop all mice once there is a cake finished.

B1. C is finished firstly when D and E are not. Ask 1,2 and 3 eat the rest of B, D and E simultaneously, the one finishes firstly is the quick one.

B2. D is finished firstly. Then 4 is the quick one.

B3. C and D are finished simultaneously. Then 8 is the slow one.

B4. C and E are finished simultaneously. Ask 5 and 6 to eat the rest of B and D respectively, if they finish simultaneously, 7 is the slow one, otherwise pick the slow one from 5 and 6.

[Former Member]

Hi

intelligence and me are two great enemies right from my childhood but me getting in to this battle being a coffee corner

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)?

answer : 5 mice together eat x/72 part of cake in 10 sec

The 2 missing characters

We know there are 26 characters in English. Now there are 8 different characters, the first person can read the first 7 of them, the second person can read the last 7 of them. The first person tells you 3 characters, and tells the second person 1 character, then the second person tells you 3 characters. Can you figure out what are the 2 charaters un-told? Of course you three may discuss a solution beforehand.

Ans : missing character is 4th and 5th

am i right ?

Regards,

Vijay.

[matt]

For the mugs, it's quite simple. You've six possibilities; each mug could be over or under. For each possibility:

a)

1. Fill mug 5

2. Pour from mug 5 into mug 3 until mug 3 is full to the brim

3. Pour remainder of mug 5 into mug 4.

4. Empty mug 3.

5. Continue at 2 until mug 4 overflows or is just under its brim.

b)

1. Fill mug 4

2. Pour from mug 4 into mug 3 until mug 3 is full to the brim

3. Pour remainder of mug 4 into mug 5.

4. Empty mug 3.

5. Continue at 2 until mug 5 overflows or is just under its brim.

c)

1. Fill mug 3

2. Pour from mug 3 into mug 5. Do it again until mug 5 is full to the brim.

3. Pour remainder of mug 3 into mug 4.

4. Empty mug 5.

5. Continue at 2 until mug 5 overflows or is just under its brim.

You'll now find that for each possibility, you'll get different results for a) b) and c) considered together. And from that you can identify the inaccurate mug and the direction of its inaccuracy.

btw, I did check for a) and b), which is sufficient to identify if it is the 3l mug or not. But haven't checked c). Conceivably, there may be another pouring sequence to differentiate between the 4l and 5l mugs, but I can't be bothered to work any further. As far as I'm concerned the problem is solved - the rest is just calculation and permutations.

matt

[hansen_chen]

Here is coffee corner, please don't be serious with the definition of genius. But it is true that I am looking for someone with very strong problem-solving skill. So it is not only for fun.

Anyway, the puzzles here are at medium level, which don't have much to do with mathematics. I also made some extremely hard puzzles. Welcome to try if someone likes challenge.

Please be confident, as long as you refuse giving up, you have chance to win. For example, the "a special mouse" puzzle, no one believed me there is a 4-cake solution at the beginning. But after 2 months, a guy in China eventually found it.

[Former Member]

> But after 2 months, a guy in China eventually found it.

So did you also tell him after 2 months that his answer was as good as yours, or is he still working at it?

> Here is coffee corner, please don't be serious with the definition of genius.

Here in the coffee corner, we are not only genius. We are also highly flexible and can change the topic at anytime without prior warning, also by massaging the question itself beyond recognition instead of just answering it...

So, because the bum moves by night and the cops only search by day, I would like to change my answer from "6" to "I don't know" now.

Please confirm whether this is correct?

Cheers,

Julius

[Former Member]

Ha, I see you really hurt some people's ego when you mention 'genius'.

[hansen_chen]

I published these puzzles last year, actually some of them are too difficult for anyone in the world. But I will not publish the solutions, since I believe some day they will all be solved by a real genius. Don't give up. Maybe your are the one.

You are welcome to try more puzzles at my blog:

http://blog.sina.com.cn/s/blog_4d1a44b30100bdxr.html~type=v5_one&label=rela_prevarticle

or Chinese version at:

http://blog.sina.com.cn/shengxiaomigong

Hansen Chen

[Former Member]

Cool, but now my answer is a "feeling lucky and sitting on the fence" answer...

I am sad that you will not provide comments, as these might point to the solutions - which no one on earth, including yourself, can work out... For example, does the program only check the presence of the bum when the cops move, or beforehand? This is one of the pitfalls of reporting.

Please post your code (the question code! => data model) otherwise the cops would need to trick the bum at each turn... so I need to bring in more cops??

Alternately, a probability calculation with 0 tolerance for error should do the trick, because it can also run on a Commodore 64 until the world energy resources are depleted because of it...

Hang on! I have a new theory based on the bum oversleeping under a pile of newspapers and then being kicked in the shins by one of his colleagues who, for a small legal waver, afterwards tips the police off about where he is...

That is how streetwise cops do it, I have heard

Cheers and thanks for the fun!

Julius

[matt]

>

> I published these puzzles last year, actually some of them are too difficult for anyone in the world....

Are you clever enough to solve them? Or is the cleverness to create the puzzles unrelated to the ability to solve them?

To be honest, the trouble I have is understanding most of the questions. I'm sure you know precisely what you mean, but it isn't evident to me.

What defines genius? There are people who can solve the Times crossword in ten minutes. There are people who can play the piano really really well, or paint, or inspire, or prove that there is no general solution to diophantine equations.

Then, while it might be a nice intellectual exercise, is it useful? Do the problems relate to real world issues? Are they valuable problems? I like working on hard puzzles - it is an intellectual stimulus, and fun. But if they're too hard, I won't expend the effort, because, ultimately, they're to no purpose. Except to declare to the world my genius. And I'd rather have other people do that, than declare it myself.

I'd also question whether there is any link to be able to solve such problems and being innovative.

[Former Member]

But I will not publish the solutions

Obviously....because you don't know the solutions. You will keep on searching for the genius for years together. That is for sure. Are you searching for genius people only from SCN or in any other way.

[ChrisSolomon]

I am still trying to figure out the apparent fascination with mice and cakes? 😃

[Former Member]

@ Bum In Cellar

As there is no condition that the Bum cannot go to the same cellar or that the police cannot search the same cellar, it is a probability proble and not minimum no. of days.

In a condition the bum switches cellar and the police look in the cellar with empty bottle, the answer is infinity..

@ Auction

A buys vase 1 at 7million

B buys Vase2 at 7 million

C buys Vase 3 at 1 million

Hope so

Edited by: Santanu Dawn on Mar 18, 2009 1:27 PM

Edited by: Santanu Dawn on Mar 18, 2009 1:28 PM

[Former Member]

> In a condition the bum switches cellar and the police look in the cellar with empty bottle, the answer is infinity..

That would only hold true if the circumference of the earch were 9 cellars long, or the police had been bribed to look in the wrong place all the time...

Cheers,

Julius

[Former Member]

I'll take an easy one:

> Puzzle: A bum in wine cellars

>There are 9 wine cellars located side by side in a street, a bum is hiding in one of of them. Everyday he would drink one bottle of wine and leave the empty bottle on the ground. Everynight, he will move to an adjacent cellar. From the day he begins to hide, the police begin to search, everyday they will search one cellar. At least how many days are enough to find the bum?

6

I would also like to to see Thomas Zloch write performance optimized code for:

> Puzzle: 3 Mugs

...scalable to infinity.

Julius

[ThomasZloch]

Part of my SDN performance optimization strategy is to only reply to questions where I know a quick answer, the rest of the time belongs to my client

[matt]

Some of these questions and more can be found [here|http://blog.sina.com.cn/s/blog_4d1a44b30100bdxr.html~type=v5_one&label=rela_prevarticle], for anyone who wants to try some alternatives. Only the questions are in English though....