riddle me this
As Captain Klot stepped out of his spacecraft, he was welcomed by five Tiddlybons, the residents of Sigma 2. Knowing that the population had a precise hierarchy, Klot asked five questions to try to discover their ranking order. To help identify them, he stuck a letter on each one. Then he asked : Was A higher than C? Was B higher than E? Was C higher than D? Was D higher than B? Was E higher than A? For each question, the second (letter) mentioned whispered a "yes" or "no" to the first (letter) mentioned who reported "yes" or "no" to Klot. However, exactly two of the five lied consistently, both in whispering and reporting answers. If all had given truthful answers, their order would have been completely determined. However, precisely two reported answers did not correspond to the true hierarchy. The reported answers were "no", "no", "yes", "no", "no", respectively. The only Tiddlybon Klot could be sure to trust reported a correct answer. What was their ranking order and who lied?
posted by aTong @ 23:10
2 comments
2 Comments:
i've got 2 possible solutions...but i can't figure out which 1 is right...
Solution:
In descending order, the ranking is B,D,C,A,E; the first two lied. With the particular questions asked, a completely determined order only arises from having exactly one "yes" or one "no" in five truthful answers. So the two wrong answers must be a "no", "no" or a "yes", "no". Only inverting each of the last pair keeps exactly one "yes". So inverting the reported "yes" means either C or D lies. If it's C, only A as the other liar gives exactly two inversions. If it's D then B is the other. For these two cases, NNNNY and NYNNN are the deduced correct answers. Only E is trustworthy being in both cases, so his correctly reported "no" gives NYNNN.
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