谜题/过河
< 谜题
过河谜题是著名的反复出现的谜题，尤其是在休闲数学中。最早已知的记录来源是 8 世纪的约克的阿尔库因（见图 1），在他的著作《Propositio ad Acuendos Juvenes》（让年轻人变敏锐的问题）中。在书中，有 3 个与过河谜题类似的问题，如下所示
以下是经典过河问题的列表
Problem 17: There were three men, each having an unmarried sister, who needed to cross a river. Each man was desiring of his friend's sister. Coming to the river, they found only a small boat in which only two persons could cross at a time. Let him say, he who is able, How did they cross the river, so that none of the sisters were defiled by other men?
Problem 18: A certain man needed to take a wolf, a goat and a load of cabbage across a river. However, he could only find a boat which would carry two of these [at a time]. Thus, what rule did he employ so as to get all of them across unharmed?
Problem 19: A man and his wife, each the weight of a loaded cart, who had two children each the weight of a small cart, needed to cross a river. However, the boat they came across could only carry the weight of one cart. Let him devise [a way] of crossing in order that the boat should not sink.
大约 1000 年后，路易斯·卡罗尔（见图 2），一位经常向孩子们展示此类谜题的解谜者，为这些古老的谜题增添了一些现代色彩。他确实写了一本关于谜题的未完成的书，在他去世后由爱德华·瓦克林整理。以下是他手稿中记录的一些谜题。
There was an old rickety bridge that connects between a town and a village. The bridges can support up to 150 pounds only and will break for even additional one pound are added to it. A young native boy coming back from town buying three beautiful cheese that he bought from town's store. The boy weighs 140pounds and each cheese weighs exactly 5 pounds. The boy knew that bridge wouldn't support him and all of three cheese. But he wouldn't leave one behind or make two trips to get all his purchase across.Being nimble in mind, he devise a way to get all of three cheeses across the old bridge in one single trip.How did he do it?
Back in Africa, three missionaries and three natives had returned to the river from their trip of mission. On the way back, two of natives engaged in a fight ; their hands were so injured that they were unable to paddle a canoe. However, they are still considered to be dangerous although they are injured. How do all people can get across the river; without natives outnumbered missionaries and ; with only missionaries and the only uninjured natives, Og to paddle the boats ?
Four people need to cross a rickety rope bridge to get back to their camp at night. Unfortunately, they only have one flashlight and it only has enough light left for seventeen minutes. The bridge is too dangerous to cross without a flashlight, and it’s only strong enough to support two people at any given time. Each of the campers walks at a different speed. One can cross the bridge in 1 minute, another in 2 minutes, the third in 5 minutes, and the slow poke takes 10 minutes to cross. How do the campers make it across in 17 minutes?
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图 1：约克的阿尔库因（位于中间） -
图 2：路易斯·卡罗尔 1863 年左右的照片 -
图 3：传教士过河
