专业数学英语60题.doc

1. A Wolf, a Goat, and a Cabbage A man finds himself on a riverbank with a wolf, a goat, and a head of cabbage. He needs to transport all three to the other side of the river in his boat. However, the boat has room for only the man himself and one other item (either the wolf, the goat, or the cabbage). In his absence, the wolf would eat the goat, and the goat would eat the cabbage. Show how the man can get all these “passengers” to the other side. 翻译： 一匹狼、一只山羊、一颗白菜和一个人在河岸，那个人需要用船把他们运到对岸去，但是船只能允许人和另一个事物(狼，山羊，或者是白菜)在船上，在人离开期间，狼会吃掉山羊，山羊会吃掉白菜。问：人如何做，才能把所以事物运到对岸去? 分析： 让M，W，G，C代表人，狼，山羊，白菜。以下是这个问题的两种解。 4.Ferrying Soldiers A detachment of 25 soldiers must cross a wide and deep river with no bridge in sight. They notice two 12-year-old boys playing in a rowboat by the shore. The boat is so tiny, however, that it can only hold two boys or one soldier. How can the soldiers get across the river and leave the boys in joint possession of the boat? How many times does the boat pass from shore to shore in your algorithm? 翻译： 有一个25人的小分队须渡过一条没有桥且又宽又深的小河. 他们看到有两个小男孩在岸边划船。船很小，只能容纳两个小孩或一个军人。军人怎样渡河才能使两个男孩留在开始的地方？在你的算法中，船从一个岸边到另一个岸边来回多少次? 分析： 6. Predicting a Finger Count A little girl counts from 1 to 1000 using the fingers of her left hand as follows. She starts by calling her thumb 1, the first finger 2, middle finger 3, ring finger 4, and little finger 5. Then she reverses direction, calling the ring finger 6, middle finger 7, the first finger 8, and her thumb 9, after which she calls her first finger 10, and so on. If she continues to count in this manner, on which finger will she stop? 翻译： 一个小女孩,数数从1到1000,使用她的左手的手指，按照下面的方式：开始她把她的拇指数为1，食指为2，中指为3，无名指为4，小指为5。然后她改变方向，数无名指为6，中指为7，食指为8，拇指为9，之后她数她拇指为10。等等。如果她继续依靠这种方式，将会停在哪个手指上？ 分析： 7. Bridge Crossing at Night Four people need to cross a rickety footbridge; they all begin on the same side. It is dark, and they have one flashlight. A maximum of two people can cross