每周数学 （二十）The Flying Quickie 20160227

每周数学 （二十）The Flying Quickie




Two bicyclists start twenty miles apart and head toward each other, each going at a steady rate of 10 mph. At the same time a fly that travels at a steady 15 mph starts from the front wheel of the southbound bicycle and flies to the front wheel of the northbound one, then turns around and flies to the front wheel of the southbound one again, and continues in this manner till he is crushed between the two front wheels. Question: what total distance did the fly cover?















The slow way to find the answer is to calculate what distance the fly covers on the first, northbound, leg of the trip, then on the second, southbound, leg, then on the third, etc., etc., and, finally, to sum the infinite series so obtained. 

The quick way is to observe that the bicycles meet exactly one hour after their start, so that the fly had just an hour for his travels; the answer must therefore be 15 miles. 

When the question was put to von Neumann, he solved it in an instant, and thereby disappointed the questioner: "Oh, you must have heard the trick before!" "What trick?" asked von Neumann, "All I did was sum the geometric series.

每周数学 （十九）闹市劫金磚；The Italian Job

 每周数学 （十九）闹市劫金磚；The Italian Job 20160221
强盗分金磚

话说当年；三个意大利强盗（阿明，阿炳；阿強）在闹市劫了一车金磚；逃离到一个孤岛, 天色已经很晚了,所以就决定大家先睡觉...

晚上阿明这家伙悄悄的起床,悄悄地将金磚分成3份, 结果发现多一个金磚子, 顺手就给埋了然后又悄悄的藏了一份,然后把剩下的金磚放回原处,最后还是悄悄地回去睡觉了.

过了会儿,另一个家伙阿炳也悄悄的起床,悄悄的将剩下的金磚分成三份,结果也发现多一个金磚, 顺手就又给埋了；然后又悄悄地藏了一份,把剩下的金磚放回原处,也悄悄地回去睡觉了.

又过了一会 .....阿強那家伙也起床了, 也做了同样的事情。

早上大家都起床了；各自心怀鬼胎的分金磚了,这次把金磚分成3分后居然还是多了一个, 只好又把它埋了.

问题来了,这堆金磚最少有多少个?