All of the monks would willingly sacrifice themselves if they knew for sure that they had a red dot. This means that on the first day, all of the monks must have seen at least one dot. Had there been only one dot the monk would not have seen any (and would have jumped knowing he had the dot), so there must be at least two monks with red dots....
Read previous posts for the solution.
I disagree. Nothing in the original riddle stated that the monks had a death-wish or the devoutness to willingly sacrifice themselves. In fact, I would argue that God would not have challenged them if it was a given that they would willingly sacrifice themselves without hesitation ... the only reason for God to challenge them (if that was the case) was to see if they were smart enough to solve the riddle: a petty God indeed, if that was the case.
Nonetheless, as to the multiple dotted monk issue, the situation would have been untenable. If you were one of the monks and saw one or more other monks with the dot, you would (a) know that those monks would not know that they had a dot, (b) have absolutely no way to communicate to them that they had the dots, and (c) wonder if you, yourself, had a dot. As the riddle is stated, there is provably no algorithmic solution for any case where the number of dotted monks (X) is any value other than one (1).
Thus, algorithmically, if the value of X is not equal to one (1), then the World would not end if and only if the monks GUESSED right, since they can not possibly KNOW how many dots were given. I doubt that the correct answer to the riddle is that the monks GUESSED correctly -- although I will concede it is possible -- in which case, no one could PROVE that their answer is "the soultion." PROOF, as you know, requires that you disprove all possible negatations of the solution. That's what the one monk solution does. No other solution posted here has met that criterion. Q.E.D.
Stating that the jump occured on the third day does not change the underlying logic, and makes solving the riddle just a little more interesting by adding an irrelevant detail. It is a classic deceptive trick, added to confuse the reader and make solving it taste a little sweeter.
