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来几道逻辑题吧

来几道逻辑题吧# BrainTeaser - 大脑工作室

y*z2008-07-08 07:07

1 楼

【以下文字转载自 Detective 讨论区】
发信人: xlzero (Megatron), 信区: Detective
标题: 来几道逻辑题吧
发信站: BBS 未名空间站 (Tue Jul 8 13:42:32 2008)
1：两个酒瓶，每个容量是8两，另有一个3两的舀子，酒瓶装满酒，舀子是空的。现在
有四个人，每个人要平均喝4两酒，如何保证。可以用瓶子喝，也可以用舀子喝
2：12个乒乓球，其中一个异常重量（不知道轻还是重），一个天平，如何称三次称出
3：100个囚犯，分100个牢房关，院子里有一盏灯，每天随机抽取一个囚犯到院子里放
风。国王对囚犯说，只要你们能保证每个人都开过一次灯，我就可以释放你们。问囚犯
如何操作才能保证被释放
4：10个囚犯被带到国王面前，国王说，面前的麻袋里有100个豆子，你们每个人可以随
机拿，最后拿最多的和最少的都要被处决。后一个人可以看到前一个人拿了多少。第一
个囚犯怎么拿才能保证活命几率最大

a*l2008-07-08 07:07

2 楼

第一题，为什么说每个人要“平均”喝4两酒？比如每人都有四分之一的机会喝16两酒
，算不算每个人平均喝4两酒？

kb2008-07-08 07:07

3 楼

4. 取平均值。10个。总会有人比他多/少。

p*k2008-07-08 07:07

4 楼

L: bottle, S: spoon, with 4 people: A, B, C, D.
L L S A B C D
8 8 0 0 0 0 0
8 5 0 3 0 0 0
8 0 3 3 2 0 0
5 6 0
2 8 1
2 8 0 4 2 0 0
7 0 3
1 6 3
0 6 3 4 2 1 0
0 8 1
1 5 3
1 5 0 4 2 4 0
1 2 3
0 0 0 4 4 4 4
i skipped some of the steps which should be apparent. seems a long process,
not sure if anyone can do better.

【在 y*z 的大作中提到】

: 【以下文字转载自 Detective 讨论区】
: 发信人: xlzero (Megatron), 信区: Detective
: 标题: 来几道逻辑题吧
: 发信站: BBS 未名空间站 (Tue Jul 8 13:42:32 2008)
: 1：两个酒瓶，每个容量是8两，另有一个3两的舀子，酒瓶装满酒，舀子是空的。现在
: 有四个人，每个人要平均喝4两酒，如何保证。可以用瓶子喝，也可以用舀子喝
: 2：12个乒乓球，其中一个异常重量（不知道轻还是重），一个天平，如何称三次称出
: 3：100个囚犯，分100个牢房关，院子里有一盏灯，每天随机抽取一个囚犯到院子里放
: 风。国王对囚犯说，只要你们能保证每个人都开过一次灯，我就可以释放你们。问囚犯
: 如何操作才能保证被释放

p*k2008-07-08 07:07

5 楼

one prisoner needs to count. for the rest of them, turn the light on
whenever he sees it is off, and do not touch the light if it is off, or if
he has already turned the light on twice. for the person who is counting,
he should turn the light off every time he sees it's on, and increase his
counts by 1. when his counts reach 198, he should know for sure everyone
else has already done it.

【在 y*z 的大作中提到】

p*k2008-07-08 07:07

6 楼

is it required that the last one has to take all the beans left?

【在 kb 的大作中提到】

: 4. 取平均值。10个。总会有人比他多/少。

h*02008-07-08 07:07

7 楼

为什么每个人要twice，按你方法，每人一次也行啊。

【在 p*****k 的大作中提到】

: one prisoner needs to count. for the rest of them, turn the light on
: whenever he sees it is off, and do not touch the light if it is off, or if
: he has already turned the light on twice. for the person who is counting,
: he should turn the light off every time he sees it's on, and increase his
: counts by 1. when his counts reach 198, he should know for sure everyone
: else has already done it.

p*k2008-07-08 07:07

8 楼

to elminate the confusion that:
(1) the light might be off at the first place and someone stepped in and
turned it on;
(2) the light is on at the first place and he is the first one stepped in.

【在 h*****0 的大作中提到】

: 为什么每个人要twice，按你方法，每人一次也行啊。

h*02008-07-08 07:07

9 楼

那只要加上一条：第一天去的人只关灯不开灯。也不计数。

【在 p*****k 的大作中提到】

: to elminate the confusion that:
: (1) the light might be off at the first place and someone stepped in and
: turned it on;
: (2) the light is on at the first place and he is the first one stepped in.

p*k2008-07-08 07:07

10 楼

yes, you are right.
i thought the date info is not available - they will not be aware of when
the king started this game. in this case, everyone turning the light on
twice seems like a clean solution. but again, you are right that
practically, everyone wants to get out there sooner :P

【在 h*****0 的大作中提到】

: 那只要加上一条：第一天去的人只关灯不开灯。也不计数。