MATH PUZZLE 1

THE MISSING DOLLAR

原文

The missing dollar riddle is a famous riddle that involves an informal fallacy. It dates back to at least the 1930's, although similar puzzles are much older.
Although the wording and specifics can alter, the puzzle runs along these lines:
Three people check into a hotel room. The clerk says the bill is $30, so each guest pays $10. Later the clerk realizes the bill should only be $25. To rectify this, he gives the bellhop $5 to return to the guests. On the way to the room, the bellhop realizes that he cannot divide the money equally. As the guests didn't know the total of the revised bill, the bellhop decides to just give each guest $1 and keep $2 as a tip for himself. Each guest got $1 back, so now each guest only paid $9, bringing the total paid to $27. The bellhop has $2. And $27 + $2 = $29 so, if the guests originally handed over $30, what happened to the remaining $1?

解读

Fallacy 谬误。
一般是指思路上的错误或者不当的逻辑推理。
例句：It was once a popular fallacy that the world is flat.
这种谬误又分两种, formal 和 informal.
Formal fallacy 指的是推理结构本身的错误。
Informal fallacy 是不当的逻辑，易误导的言辞，混乱的思路引起的错误。
你觉得上面这个例句的谬误是属于formal 还是 informal 呢？
当然这种谬误都不是有意的。如果是蓄意的，恶意的，在中文里我们称之为诡辩， 相应的英语是sophism.
Bellhop 旅馆侍者。
旅馆的前台一般都有一个铃铛（bell）, 当你按铃的时候就有人（跳，jump, hop）出来为你服务。
有很多的职业的名字都很好玩， 比如
Busser: 餐馆或咖啡厅收拾桌子的人
Honey Dipper: 钻下水道井盖的维修工人（戏称）
Chick Sexer: 分辨小鸡性别的人
Eggler: 买卖鸡蛋的商人
Hairapist: 美发治疗师。理发师给人理发很多年了， 听了很多八卦，于是可以一边理发， 一边给人提供建议和生活的哲理的人。这个词应该是Hair-stylist 美发师和 Therapist 心理医师的合体。

答案

这个puzzle犯的逻辑错误是把收入和支出混在一起了。一个好的会计（accountant）会把账本分开算。

	收入	支出
Clerk	$30-$5=$25
Bellhop	$5-$3=$2
Guests		-$30+$3=-$27
Total	$27	-$27

旅店收了$30元退了$5元，收入为$25元。
侍者$5元只还了$3元，往自己包里放了$2元。收入为$2元。
目前为止总收入为$27.
三个客人共出了$30元， 但是每人又收回$1（$1x3=$3）元，总共支出为$27元。
收入和支出相等，所以并没有钱流失。