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
I claim to be younger than myself (but I lie) by Steve Herman)
My reaction to this ploy is partly explained in my last reply to Charlie concerning the implications of "liars" as presented in this genre. Only propositions may be either true or false. "I am younger than myself" does not express a proposition, therefore it is merely a noise made by one of the participants -- and it is not defined what noises a liar (or a knight) may make, or how they should be construed (if at all). If Brenda says "I feel younger today" we may treat this as an emotive outburst (if we bother at all) or as a (necessarily false) report of her introspected state. This issue does not arise when one of the five is stating an age comparison with any of the other four.
Your original method of solution is ingenious, and seems to arrive at the unique solution. My approach is to develop an algorithm for a full search, encoding the constraints as they are expressed. Since the greater interest is in the variety of methods of solution, than simply getting an answer, I am glad you explained your reasoning.
re: I claim to be younger than myself (but I lie)
