Abby, Brenda, Carol, Diane and Emily are all of different ages. Two are liars and three are knights (knights always tell the truth; liars always lie).
Brenda claimed to be younger than Emily.
Carol claimed to be younger than Abby.
Carol claimed to be younger than Brenda.
Carol claimed to be younger than Diane.
Carol claimed to be younger than Emily.
Diane claimed to be younger than Brenda.
Diane claimed to be younger than Carol.
Diane claimed to be younger than Emily.
Emily claimed to be younger than Abby.
Emily claimed to be younger than Diane.
There were two other, similar, statements made, besides the ones metioned above, and in fact those were the only other statements like that that could be made.
That might be a little ambiguous, but resolving this ambiguity is part of the fun, and you can do it.
Who were the two liars and what was the order of their ages?
You can even fill in the two unheard remarks:
_______ claimed to be younger than _______
_______ claimed to be younger than _______
(In reply to
re: No ambiguity at all by Charlie)
I wonder whether anyone would have thought of that as an ambiguity. Perhaps liars can lie about their age, but could they say they were younger than themselves? Of course, if you asked Brenda if her name was Brenda, I suppose she would have to say No. If one asked "Do you really mean that?" , how would she respond?? Suppose Brenda said "I am younger than Springtime" what then? If you allow reflexive comparisons, you would be adding a lot more than two candidate statements. 1480 was carefully worded not to present these options (I think).
It seems to me there are inherent difficulties in these "knights and liars" puzzles which assume some unstated "rules of the genre" to avoid absurdities (and, when stated, still seem oblivious to the issues of logic). Another puzzle of that ilk (a "voting/polling" situation) was posted here about a week ago, and seems tangled in its own verbiage (even though it claimed to have been vetted in some way). It failed to address the ambiguities of inclusive/exclusive disjunction, for one. It burked the issue of the "intention to deceive" as a component of lying; implicitly a liar (in the problemacists use) is akin to the knight: from any statement (and the knowledge that the speaker was a "liar") one would infer the truth of the converse of the statement. This would be the equivalent of treating the liars as dyslexics, who simply got their Ja/Nein reversed.
One does not "solve" a puzzle which does not present a clear description (unless one simply stipulates an interpretation and then solves that). Others may play with these conundrums, but are not solving puzzles. Perhaps the parallel is more to those crosswords where the "clues" cause groans rather than "aha".
Suppose you had two of your liars. The first said "This statement is false" and the second said "This statement is true."
Then the first said "That second statement is false," and the second said, "That first statement is true." Similarly if one said "I am younger than myself" what proposition would that person be asserting or denying?
re(2): No ambiguity at all
