# Battle of the Marks

royalchicken
Posers and Puzzles 21 Jun '03 22:52
1. royalchicken
CHAOS GHOST!!!
21 Jun '03 22:521 edit
(Puzzle the fourth.)

Knowing that he cannot hope to win the Battle of the Marks over the chessboard, royalchicken issue the following challenge to T1000 (and anyone else who'll solve it).

Royalchicken says that there are two identical twins, let's call them Akribis and Lathemenos, who behave in an odd way. Akribis has a perfect understanding, and always tells the truth. This means that he believes all true statements to be true, and false ones to be false, and he always tells the truth. Lathemenos believes all true statements to be false, and false ones to be true, but he always tells what he would consider a lie. For example, when asked Is 9*7 = 63?, they would give identical responses-Yes. Akribis would think he was telling the truth, Lathemenos would consider his response a lie. My question is whether a series of yes-or-no queries can be devised to tell which is Akribis and which is Lathemenos, and if so, specify this series of questions.

Enjoy. Also, upon further reflection, I note that certain philosophical questions could arise, so there are some answers that are better thn others (hint).
2. 21 Jun '03 23:171 edit
Oh you cruel man you. I shall return in 3 days (having not revisited this thread to avoid seeing the answer should/when someone posts it) and answer as to whether or not I've worked it out.

At this early juncture I would say that me being successful is not, so to speak, a runner that deserves a great deal of backing...

T1000
3. bbarr
Chief Justice
21 Jun '03 23:27
Originally posted by royalchicken
(Puzzle the fourth.)

Knowing that he cannot hope to win the Battle of the Marks over the chessboard, royalchicken issue the following challenge to T1000 (and anyone else who'll solve it).

Royalchicken says that there are two identical twins, let's call them Akribis and Lathemenos, who behave in an odd way. Akribis has a perfect understanding, a ...[text shortened]... hilosophical questions could arise, so there are some answers that are better thn others (hint).
Ask them both if their name is Lathemenos. Whoever replies 'yes' is Lathemenos. As with most of these puzzles, self-referentiality is the key.
4. royalchicken
CHAOS GHOST!!!
22 Jun '03 00:58
You are correct on both counts. However, think of this, and why I added the caveat. Another question would be to ask &quot;Are you the truth-teller with a correct grasp of reality?&quot; Akribis would say yes, and Lathemenos, believing himself to be the person thus descibed, would 'lie' and say &quot;No&quot;. So again, Akribis would say yes. THis is fine if they are perfectly logical automatons, but suppose they can also do some pondering of their own. Say Lathemenos recieves the above question. Because he honestly believes he has a correct grasp of reality (because he thinks false things are true), he will think he IS the truth-teller, and, and, if he reflects further, will find that he has thought &quot;Yes&quot; and said &quot;No&quot;. He will therefore deduce that he is a liar, which is correct, in violation of the premise that he thinks every false statement is true and every true statement is false.
5. royalchicken
CHAOS GHOST!!!
22 Jun '03 17:43
Note that, according to a friend of mine who studies Greek, &quot;Akribis&quot; means &quot;true&quot; and &quot;Lathemenos&quot; &quot;false&quot;.