一道非常強大的智力測試題～！！

12d3

在一個監獄裏，有101個犯人，被關在10１個獨立的牢房裏，互相無法通信。
　　　　
　　　　一天，召開全體囚徒大會。國王大赦，給大家一個機會。
　　　　
　　　　條件：在當天夜裏，會有人來把每間牢房門的正面隨機地刷上黑色或者白色，顏色的選擇是同等概率隨機的（比如用拋硬幣的方法決定門上該刷黑色還是白色），犯人們都不知道自己門上被刷了什麼顏色。
　　　　
　　　　第二天早上，犯人會依次被叫到典獄長辦公室裏。在走出牢房時，犯人都有機會看見所有其他人門上的顏色，但是因為他自己的牢門是開著的，門的正面靠著牆，所以他看不見自己門上面的顏色。在辦公室裏典獄長讓每個囚犯猜自己門上的顏色，只能回答說“黑色”或者“白色”。然後犯人被帶回牢房，關好門後，下一個犯人再被叫出詢問。如此這般，直到所有人都被叫出來一次為止。
　　　　
　　　　注意：在典獄長辦公室裏犯人是看不到前面其他犯人的回答的。
　　　　
　　　　機會：最後典獄長統計一下所有犯人的回答。如果猜對自己門上顏色的犯人數過半，那麼就釋放所有犯人。如果不過半，每個犯人都只好把牢繼續坐下去。
　　　　
　　　　問題：囚徒大會後給大家20分鐘時間討論，囚徒們能找到方法麼？


我大膽推斷, 呢個問題係冇答案, 大家認唔認同?

anttiniemi2000

all prisoners should guess the same colour.  as the choice of the colour of the paint is random, the white:black ratio is likely to be 1:1.  however, it will not be the actual case and there should be more doors with one colour than the other.  if the prisoners are lucky enough, they will pick the correct colour.  i know it will not the 'real' answer, but this is a fair gamble and not a bad answer.

yamits

Since everyone sees every other person's colour on the way to the King, they should each tally up the amount of black-coloured doors and white-coloured doors and tell the King the colour that are on MOST doors. E.g. If a prisoner sees 52 black doors then he should answer 'black'. Using this method, the majority of prisoners will get their colour right.

This method will absolutely work for all situations except for one. The exception is when there are 51 whites and 50 blacks (or vice versa). In this case, all prisoners with black doors would be wrong and and some of the prisoners with white doors (facing a 50-50 proposition) will also be wrong -> Majority will be wrong.

However the chances of painting 51 whites and 50 blacks (or vice versa) is extremely small:

Probability = (101 C 50) / 2^101 = slightly less than 8%

Thus this is likely the optimum strategy. (RIght? LOL)

Could Mr Poster plz reply to see if this analysis is right?