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=>[color:"#3A495A"]Still asuming the 2 monks: He can only know it if the other monk doesn't jump on the 1st day either (then the both monks have a dot, and they would jump on the 2nd day). If one of both monks jump on the first day, then the one that jumped only has a dot on his head.
Now back to the normal story, there they jump on the third day,so meaning that there are 3 monks having dots on their heads. So they jump when the number of dots that they see, overrides it with one.[/color]


Fair enough, I'll take that as the correct answer <img src="/ubbthreads/images/graemlins/winkwink.gif" alt="" /> I'll post an "extended" explanation now. Well done! <img src="/ubbthreads/images/graemlins/up.gif" alt="" /> <img src="/ubbthreads/images/graemlins/smile.gif" alt="" />

-> [color:"#3A495A"]
Day one. Suppose there is one monk with a dot.

All monks are standing at the cliff. The monk with the dot doesn't see anyone with a dot, so, since he knows there is at least one monk WITH a dot, he knows he's the one, the only one. So, at 12:00 pm, that one monk would jump.

However, no one jumped the first day, so we know one thing for sure now: there are AT LEAST two monks with a dot.

Day two. We know there are at least 2 dots. Suppose there are exactly 2 dots.

Both monks with a dot, only see one monk with a dot. At that moment they KNOW they have a dot as well, since they know there must be at least two dots. No doubt, they are number two. No doubt, they jump at 12:00 pm.

But no one jumped at day two. Conclusion: there are AT LEAST 3 dots.

Day three. We know there are at least 3 dots. Suppose there are exactly 3 dots.

Each of the three monks with a dot only see 2 dots, so they each know they are number three. They will jump at 12:00 pm.

And they jumped, so there were exactly three monks with a dot, leaving the other monks relieved, because they now, finally, know for sure they don't have a forth dot.




Feel free to question this solution, and check if it is really correct <img src="/ubbthreads/images/graemlins/biggrin.gif" alt="" /> Most people don't believe it because there were 3 dots from the beginning, and by the end of day one, the monks with a dot already knew there were AT LEAST 2 dots, and the other monks even know there were at least 3 dots! So they could've jumped on day two! Right? No, wrong <img src="/ubbthreads/images/graemlins/tongue.gif" alt="" /> Figure it out <img src="/ubbthreads/images/graemlins/biggrin.gif" alt="" />

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Mr Kej, Second Member of the Guild of Off-Topic Posters *** Visit Aviorn's Inn, my Divine Divinity fansite ***