"Good afternoon, Mr. Phelps. The Society of Logicians have recently discovered a plot to overthrow the friendly government of Uwalahooloo. Your mission, should you decide to accept it, is to return to Uwalahooloo and appropriate the alabaster crown, a totem in the keeping of the hostile chieftain. Bereft of this artefact, the chieftain will lose his standing with local warriors, and his plot will fail.

You will find the crown, unguarded, somewhere along one of the island's two paths, one coloured red, the other green. The false path is to avoided at all costs, as it leads through deadly quicksand.

Intelligence reports the island to be inhabited by three natives, each one a liar or a knight. The natives are identical in appearance, but may be distinguished by their differing garb. The native in green is a monolingual speaker of language g, while the native in red a monolingual speaker of language r. The native in yellow is also monolingual, but we have not been able to determine which of the two languages, either g or r, he speaks.

You may assemble the natives and pose one question per day. (The same question to each native). As is usual on Uwalahooloo, the questions have different meanings in the two languages. After responding, the natives will retire out of sight until the next day.

Be warned: the natives delight in tricking logicians: when out of sight the yellow native may change clothes with the native with whom he can communicate.

Finally, you need to be alerted to the fact that the natives are only conditionally friendly. They will patiently respond to two queries, but if you try to ask them a third question, they will their lose patience and have you over for dinner (typically covered in barbecue sauce). We therefore urge to you consider carefully which questions to pose.

Here, now, are the candidate questions with their alternative interpretations in languages g and r:

Hvilket?

g: Is the road with the crown the same colour as one of the other two natives' costumes?

r: Are the other two natives able to communicate?

Spoergsmaaler?

g: Is the yellow native the same truth type as the native with whom he can't communicate?

r: Are the other two natives of the same truth type?

Bliver?

g: Are the other two natives able to communicate?

r: Has there been a costume change?

Ud?

g: Has there been a costume change?

r: Is the road with the crown the same colour as one of the other two natives' costumes?

Should you be discovered in Uwalahooloo, the SL will deny any knowledge of your mission. Good luck, Jim. This tape will self destruct in 10 seconds."

Derive a syllogism, based on native responses, for the road containing the crown.

An examination of the two questions to ask are "Bliver?" followed by "Ud?" eliminate it from consideration as we can not determine the road color if we get the following day-one and day-two responses from the natives dressed green, red, and yellow:
YYY YNN, YYN NNN, NYY YYY, NYN NYY.

From the other possible responses we can determine the color of the road due in part from the following analysis:
From the first day of questioning, as there has not yet been a costume change, we know whether the red-dressed native is a Knight or Liar by his response to the question "Bliver?". A "Yes." to the question would indicate he is a Liar and a "No." would indicate if he is a Knight.
The same is true of a yellow-dressed native r speaking native. If the yellow-dressed native spoke g, then, identically, the same responses would apply to identifying his truth type. A "Yes." to the question would indicate he is a Liar and a "No." would indicate if he is a Knight.

Edited on April 25, 2008, 2:59 am

Posted by Dej Mar on 2008-04-24 00:24:02