白骨精组入门, 来自老美的超级智力测验题

下面的许多题目来自著名的Ron Hoeflin的超级智力测验. 按照Ron Hoeflin的说法, 如果你能在前11到题里做对6道, 你的智商超过137, 好于百里挑一了.一般程序员智商可能也就120左右.

做题没有时间限制, 除了你不应当让别人帮助或者去网上找现成答案外(目前找到现成答案的可能性很小的, 别费事了), 也没有任何其他限制.  另外, 题目比较难, 你可以先把本网页保存在本地, 慢慢做. 看看你能做出几道. 如果你做出来了, 请不要把结果发布到网上,  否则, 别人就无法客观的测试了.  另外这也是Ron Hoeflin的请求.

做题的答案可发站内消息给我, 请你起码尝试5道题后再发.

背景：

Ron Hoeflin 是美国许多著名的超级智力测验的设计者, 是几个高智商者协会的发起人. 其中包括, TOPS(百分之一尖子), OATH(千分之一尖子), Prometheus(三万分之一尖子), Mega(百万分之一尖子) 等.
智商的定义，对于儿童和青少年，智商是智力年龄/实际年龄，对于成人，智商是按照智力在人群中的统计分布通过归一化来定义的，智商100定义为分布的平均值，89-111被定义为包括了人口中的50%。 这样，0-137包括了人群的99%. 如果你的智商>137, 那你就算是百里挑一了。

 

智商并不代表人的全部能力，但是对于科学与技术来说，基本上，人类的所有创造发明与智商低于120的人都没有什么关系。

 

Kakrat

 

1. 最少需要几个小方纸片(正方)才能组成右边的图形. 注意, 纸片大小可以不一, 被盖住的边看不见.
2. Suppose that three intersecting(相交) rectangles(矩形) are drawn on a flat(平) surface(面). What is the maximum number of completely bounded areas, not further subdivided, that can thereby(因此) be formed, considering only the sides of the rectangles as boundaries? (The figure to the right illustrates two intersecting rectangles.)
3. Three mutually intersecting circles (as illustrated to the right) can yield a maximum of seven completely bounded areas, counting only areas that are not further subdivided. What is the maximum number of completely bounded areas not further subdivided that can be obtained using three mutually intersecting circles plus two triangles?
4. The figure illustrating this problem shows a scale(天平) for weighing objects, consisting of a lever resting on a fulcrum(支点) with weighing pans at each end of the lever equidistant from the fulcrum. Suppose that the objects to be weighed may range from 1 to 100 pounds at 1-pound intervals: 1, 2, 3, ..., 98, 99, 100. After placing one such weight on either of the two weighing pans, one or more pre-calibrated weights are then placed in either or both pans until a balance is achieved, thus determining the weight of the object. If the relative positions of the lever, fulcrum, and pans may not be changed, and if one may not add to the initial set of pre-calibrated weights, what is the minimum number of such weights that would be sufficient to bring into balance any of the 100 possible objects?
5. A certain lock(船闸) for raising and lowering barges(船) from one river level to another is a rectangular parallelepiped(矩型体) 200 meters long, 50 wide, and 20 deep. A barge is floating in the lock that is also a rectangular parallelepiped measuring 80 meters long, 25 wide, and 5 deep. The barge, containing 3,000 barrels(桶) of toxic(有毒) chemicals, displaces(排水) 8,000 long tons of water. The water has a density of one long ton per cubic meter. Each barrel is watertight, with a volume of one cubic meter and a weight of two long tons. A group of terrorists render the lock inoperable and attach a time bomb to the side of the barge set to go off in three hours. The barge contains elevators for moving barrels quickly to the deck, but the crew(船员) is too shorthanded(人手不够) to roll the heavy barrels up an inclined(倾斜的) plane in the time allotted(允许的). The deck(甲板) is only ten centimeters below the top edge of the lock, from which the barrels could be rolled to dry land. If no water is entering or leaving the lock, how many barrels at a minimum would have to be rolled into the water in the lock in order to raise the level of the barge so that its deck would be even with or slightly above the top edge of the lock so that the remaining barrels can be rolled to dry land?
6. In going from square A to square B in the figure, what is the maximum number of squares that a chess knight(马) could touch, including A and B, if the knight makes only permissible moves for a chess knight (consult a book on how to play chess if in doubt), does not touch any square more than once, and does not go outside the 16 squares shown? (knight:马, 走日, 和中国象棋同, 但是是在格中, 而不是格点上.)
7. Suppose a modified version of the dice(骰子)game is played with two regular (i.e., perfectly symmetrical) dodecahedra(正十二面体,面为正五边形). Each die (骰子) has its sides numbered from 1 to 12 so that after each throw of the dice the sum of the numbers on the top two surfaces of the dice would range from 2 to 24. If a player gets the sum 13 or 23 on his first throw, he wins. If he gets 2, 3, or 24 on his first throw, he loses. If he gets any other sum (his point), he must throw the dice again. On this or any subsequent(后续) throw, the player loses if he gets the sum 13, and wins if he gets his point (the sum in previous throw), but must throw both dice again if any other sum occurs. The player continues until he either wins or loses. To a hundreds of one percent(近似到万分之一), what is the probability(概率) that a dice thrower will win with this game?
8. Suppose a tetrahedral-shaped(正四面体形) crystal is formed, like a giant pile of apples or oranges at a greengrocer's store (果菜店), consisting of one atom on the top layer, three on the next-to-top layer, six on the third layer, ten on the fourth layer, and so forth as illustrated below(如下所示). If there are exactly 1,000,000 layers, specify the total number of atoms in the entire crystal. Give an exact answer, not an approximate(近似) one or a formula for making the calculation. (不得编软件去算)
9. Suppose 27 identical cubical chunks(块) of cheese(奶酪) are piled together to form a cubical stack, as illustrated to the right. What is the maximum number of these cheese chunks through which a mouse of negligible(可忽略) size could munch(啃) before exiting the stack, assuming that the mouse always travels along straight lines that pass through the centers of the chunks parallel or perpendicular to their sides, always makes a 90 degree turn at the center of each chunk it enters, and never enters any chunk more than once?
10. Suppose there are ants(蚂蚁) at each vertex(顶点) of a triangle and they all simultaneously(同时地) crawl(爬) along a side of the triangle to the next vertex. The probability that no two ants will encounter(遇见) one another is 2/8, since the only two cases in which no encounter occurs is when all the ants go left, i.e., clockwise -- LLL -- or all go right, i.e., counterclockwise -- RRR. In the six other cases -- RRL, RLR, RLL, LLR, LRL, and LRR -- an encounter occurs. Now suppose that, analogously(类似的), there is an ant at each vertex of a cubic and that the ants all simultaneously move along one edge of the cubic to the next vertex, each ant choosing its path randomly. What is the probability that no two ants will encounter one another, either en route(在路上) or at the next vertex? Express your answer reduced(化减) to lowest common denominators(最小的分母), e.g., 2/8 must be reduced to 1/4.
11. 假设已知一个盒子中有10个围棋子. 这些围棋子是按照掷硬币的结果来放入的. 如果硬币正面朝上, 就放黑子, 反之放白子. 而硬币朝上还是朝下的概率是完全相等的. 现在, 从盒子中完全随机的取十次棋子, 每取一次, 记录下棋子的颜色, 然后再放回去, 从新摇匀, 以保证下次取的棋子仍然是完全随机的.  现在, 取的结果刚好是10个白子, 那么, 盒子中实际上全是白子的几率是多大?  结果近似到万分之一就可以了.
12. 用 Z= Encrypt(X,Y) 表示以X为密钥对Y进行加密, 结果为Z, 问题是, 假使 C=Encrypt(P,P), 那么对于一个一般的加密函数Encrypt, 是否不存在 另外一个P2!= P,但是Encrypt(P2,P2) = Encrypt(P,P)?    注意, 我说的是一般的加密函数, 也就是说所有的满足以下条件的函数: a. 对与任何key, 如果P2!=P, 那么Encrypt(key,P2)!= Encrypt(key,P) b. 用Decrypt 表示和Encrypt对应的解密函数, 对与任何key, 如果P2!=P, 那么Decrypt(key,P2)!= Decrypt(key,P).   注意这个命题里的所有这两个字.
13. 在asp.net的应用中需要多次使用一个固定的密码进行加密运算. 通常作加密的步骤是, 先产生一个加密服务类实例, 然后调用该实例提供的服务. 产生加密服务类实例是个很费时的操作, 另外, 已知加密类的所有静态函数是thread safe, 而其成员函数是thread unsafe的.  如何优化以克服产生加密服务类实例费时的问题? 对这个问题的解法可以进一步推广成为一个pattern, 请说说你怎样设计这个pattern, 说出其中应当主要包括的class 或 /和interface或 /和 delegate, 并举例说明对任何一个具体这类问题如何应用你的pattern.