In a remote island there are only two types of people that live on it, Knights and Liars. Knights always tell the truth. Liars always speak falsely.
Five suspects are interrogated in connection with a murder. Their statements are as follows:
Al: "Cal and Dan are lying."
Ben: "Al and Elmer are lying."
Cal: "Ben and Dan are lying."
Dan: "Cal and Elmer are lying."
Elmer: "Al and Ben are lying."
Which suspect do you know for certain to be a liar?
Logical solution
AL  Means A is lying
AT  Means A is telling the truth
1)A – C & D are lying , 2)B – A & E are lying, 3)C – B & D are lying, 4)D – C & E are lying, 5)E – A & B are lying
Case 1 – A is telling the truth  AT
From 1) CL , DL, From 3) BT, From 4) ET, From 2) AL,EL is false, From 5) AL, BL is false
Hence A is Lying for sure
Case 2 – B is telling the truth  BT
From 2) AL, EL, From 1) either CT or DT or CT&DT, From 5) AL & BT is true, From 3) CT is not possible if CL then DT is only possibility, From 4) CL & EL is confirmed
Hence B could be telling the truth
Case 3 – C is telling the truth  CT
From 3) BL, DL, From 2) either AT or ET or AT&ET, From 4) ET & CT is true, From 1) CT & DL is true & From 5)AL & BL is true
Hence C could be telling the truth
Case 4 – D is telling the truth  DT
From 4) CL, EL, From 3) either BT or DT or BT&DT, From 5) either AT or BT or AT&BT, From 1) DL and AL hence BT From 2)AL & EL which is true
Hence D could be telling the truth
Case 5 – E is telling the truth  ET
From 5) AL, BL, From 1) either CT or DT or CT&DT, From 2) AL, ET, From 4) DL, CT, ET is solution, From 3) BL, DL and CT is confirmed
Hence E could be telling the truth
Hence Al is the only liar.

Posted by Salil
on 20130228 00:49:44 