1. five holes in a row, in which a hole in possession of a fox. Each night, the fox will jump to a neighboring hole; each day, you are only allowed to check one hole. How can we ensure that the fox will eventually be caught?
2. There are 23 coins on the table, 10 face up. Blindfolded your eyes (you can not distinguish between positive and negative), and how divided into two groups, so that the two face up as many coins?
3. There are two sets of coins, a set of 100, another group of 200. Both A and B are to take, it may take any of a number selected in a group (can not take), or take a like plurality of (for example each take 100) in both groups. Who took the last win count, acquire or win after win to take? What kind of strategy?
4. You and eight companions came to the ancient temple, we go deep into the center of the building. The results of two people accidentally touched the altar authorities, poison gas was sprayed his face, while the temple's walls began to shake, antecedents are blocked. You quickly fled along the tunnel outside the temple, they encountered four fork in the road. Only one way leading to the outside, but do not know which article. Wall collapse soon, you escape remaining one hour, each channel is known finish time is 20 minutes. So you can be all divided into four groups (including their own), to ascertain the road, return to this fork in the collection, and from a total of 40 minutes. You can then use the remaining 20 minutes to escape from the right channel.
Unfortunately, because of the toxicity of the two poisoning episodes, may tell the truth, it may tell lies; one of them might lie, it could both lie. And at that time the dark environment, we do not know what the two poisoning. I ask, how should you grouping, to ensure that the four routes to determine the correct path?
5.
He was given A, B, C three playing cards ,
the teacher said: "You get three numbers and are 14, you can only look at his cards, guess what the other two got the numbers right? "
A: "I only know of two ethylene-propylene numbers must be different."
B of A said: "I know I told you the numbers must be different."
C: "That's so I know the two of you figure it out."
I ask, what figures to get propionate of it?
6. U2 choir to be rushed to the concert venue, essential way across a bridge, four people from the same side of the bridge, you have to help them reach the other end, the sky was dark, and they have only a flashlight. Up to two people at once across the bridge together, and when the bridge must hold a flashlight, so you have to bring someone to bring a flashlight, and from both ends of the bridge. Flashlight is not used to transfer the lost way. Four people walking speed each different, slower speeds if the two counterparts places shall prevail. Bono needs to take 1 minute to cross the bridge, Edge need to spend two minutes across the bridge, Adam need to spend five minutes across the bridge, Larry need to spend 10 minutes across the bridge, they could not do more than 17 minutes across the bridge?
7.60 classmates surrounded by two circles inside and outside games, the same as the center of the two circles of different radii. Inner ring with 30 students from each class and the second class of 15; the outer ring is 30 students, all from the class or second class, but the number of each class do not know. Outside the inner ring face down, face down in the outer ring, at the beginning of all are relatively positive. Students held stationary inner ring, an outer ring students started simultaneously at the same speed move clockwise around the outer circle. Little said: during the game, there is a moment at least, the outer ring has no less than 15 students facing this class of students. Will Little said is correct?
8. a closed village has 100 residents. One Christmas, all residents presented a gift to each other each other, every resident are sent and received 33 hats and 33 pairs of gloves and 33 pairs of shoes. If any two people give each other gifts that are of the same type, whether residents will be able to find three, just presented three different gift between any two?
