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Question

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.
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

Answer 1

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.