chinese emporer 2

[WorkHorse]

chinese emporer2 aha!!

Same as chinese emporer 1:

A chinese emperor had to choose a new adviser amongst 3 sages, all of them equally wise. He placed a problem to them: "To choose one of you, you'll play a simple and fair game: In this sack there are 3 white balls and 2 black balls. Each of you will be blindfolded and will pick one ball and place it on your head. After that, the blindfolds will be removed and each one in turn will try to guess the colour of the ball upon his head, by observation of the other picked balls. However, beware. You may pass your turn in guessing, but if you state a colour and fail, you're disqualified. This way I'll learn which one is the most intelligent amongst you" The sages talked briefly to each other and promptly refused: "Dear lord, it's of no use, since the game is not fair. The last one of us to guess in the first round will know the answer." and the sages promptly demonstrated this to the emperor, who was so amazed by their wits that he appointed all 3 has his advisers. Could you demonstrated it ?

Now chinese emporer 2:

But then...another sage came forward and proved to the king that if the sages really are as smart as they seem, sage 3 would never even get a guess because sage 1 or sage 2 would always be able to guess the correct answer. He explains the logic to the king. The king fires the other three sages and hires the smarter sage with three times the pay. How did he explain this?

[kedaman]

erm.. didn't i already explain this in the first one..

[NotLKH]

The Next morning, the king wakes up with a start.

"Now How the Heck did my new sage even know the question! He came in after I asked it!"

Immediately, he summons his guards and has the sage locked up for being a spy. He then hires 2 more security officers, and spends the rest of his budget on High speed internet, so all his questions can be answered by google.

The End.

Now, Back in the dungeon, the Officer in charge poses a question to the new sage, and all the other lifers.

"Each one of you will be placed 1 at a time in a cell which only has a light and a light switch..."

[fundu]

WorkHorse I think U were not fully OK when U extended the question.

I can give an example to disprove that.

Lets suppose the combination WWW.

Then Sage 1 has 2 pass if he see2 white balls as he can't conclude.

It sage 1 passes, the combination can be either WW or WB or BW. But as sage two can see that sage 3 has a white ball, the middle option is out but still WW and BW combinations are left. Though he can see that sage 1 has a white ball but still he can't conclude with that that what colour he has. Moreover sage 1 can even have a black, still sage 2 can't conclude.

Thus the chance will definitely come 2 3rd sage ion such a cse who will concllude.

Think again before posting such questions (puzzles) when U don't know the correct solution.

[kedaman]

I don't think this is an extension, its the same question - there was no rule that a sage cannot guess and thus must pass. Not in this one either for that matter.

Is anyone hearing what i'm saying?

[fundu]

Don't get excited. How can a sage guess if he is not sure because as the question said that if in case his answer is wrong he will not get another chance.

Moreover if I think logically a contestant of that post (and espacially at the time of chinese emperors) should only say something if he is sure. They are answerable for all there acts and are looked after the idols in their countries. Only a someone like you can afford to guess in the situation

[kedaman]

If risks were not worthwhile none would ever be taken.

[fundu]

One should take risks in life. Though it is advisable to take calculated risks only, but one can take risks otherwise also. It totally depends when, where & for whom U R taking the risk.

THINK of the position for which U R asking these sages this question. And then think how U can ask them to guess based on probability or guess. Such a thing cannot be covered under the shadow of a calculated risk. Infact it is not even a risk. People at that position are not supposed to use intution, imagination or probaility. It is blunder to even think so when Ur decisions can change the fortunes of the people of the country. Someone (of this stature) who for his own profit can say anything based on guess or intution, should never get such a post as then you can even bribe such a person for any other decision of your help. After all it is a matter of their intelligence and self esteem

[kedaman]

how much are you willing to bet on this, I play sage 1 and sage 2 while you play sage 3.

[WorkHorse]

Yeah kedaman! Sorry, I read through your solution again and you did answer this question. I was expecting someone to come up with the solution I gave so that I can then go on to this question, but you were way ahead of me. And you solution to this problem is better than mine. I worked out all possible combinations adn then the probability of each. Listing the possible combos of the five balls is much easier. Very cool. And of course a sage would guess and never pass because there is no penalty and the sage would paly the odds to win.

So, to recap: there are seven possible combinations, but the combinations with 2 white and 1 black are twice as likely. See kedamans post, or calculate the combinations and possibility of each, or label each ball W1 W2 W3 B1 B2 and list all the combinations for yourself, or make a small program to check random samples, or do whatever. You end up with the possibliities like kedaman said (when looking at the three balls picked, twice as many chances for cases when there is 2 white and 1 black). Here they are:

1 WWW
2 WWB
3 WWB
4 WBW
5 WBW
6 WBB
7 BWW
8 BWW
9 BWB
10 BBW

If Sage 1 sees BB, it must be case 6. Chooses white.
If Sage 1 sees BW, white is correct for 4 cases (2, 3, 4, 5) and wrong for 1 cases (9, 10). Chooses white.
If Sage 1 sees WW, white is correct for 1 case (1) and wrong for 2 cases (7, 8). Chooses black.

Let's see how he did:

1 WWW B LOSE
2 WWB W WIN
3 WWB W WIN
4 WBW W WIN
5 WBW W WIN
6 WBB W WIN
7 BWW B WIN
8 BWW B WIN
9 BWB W LOSE
10 BBW W LOSE

He win on 7 out of ten, even when guessing. If he lost, Sage 2 gets a crack, but there are only three cases left:

1 WWW B LOSE
9 BWB W LOSE
10 BBW W LOSE

Now it should be clear that Sage 2 can guess the correct answer:

If Sage 2 sees BB, it must be case 9. Chooses white.
If Sage 2 sees BW, it must be case 10. Chooses black.
If Sage 2 sees WW, it must be case 10. Chooses white.

Let's see how he did:

1 2
1 WWW B LOSE W WIN
2 WWB W WIN
3 WWB W WIN
4 WBW W WIN
5 WBW W WIN
6 WBB W WIN
7 BWW B WIN
8 BWW B WIN
9 BWB W LOSE W WIN
10 BBW W LOSE B WIN


Sage 2 will always win if Sage 1 does not.

So you see that if the sages really were as smart as kedaman, they would have told the king that the game would be over by the second guess, not the third.

I thought three might be another version whether the first sage tries to fake out the other sages when he isn't certain. kedaman beat me to that as well showing that the sage would never guess. It turns out that Sage 1 could never fake out bothother sages in the hopes that it would go to round two (in which case Sage 1 would always win if he guessed wrong in the first round because he would only have to give the opposite answer). But it doesn't work out, even if Sage 1 tries to fool the others in some way, at least the third sage would always be able to answer correctly. So, no more sages.

[Nucleus]

I only read this thread after the first one, and yes I was listening Ked!

The problem is that sometimes it is difficult for people to consume your content even though it does give the answer. Perhaps a simple analogy at the end is a way to make people understand?

[kedaman]

Yeah I think I need to work on it, stupid of me to expect anyone to understand what i'm rambling about