Argentine, Brazil, Colombia, Dominican Republic and Equator competed at the Olympic Games, placing first through fifth in an event. They said:

Argentine: "I was not last."
Brazil: "Canada got the bronze."
Canada: "Argentine ended behind Equator."
Dominican Republic: "Equator got silver."
Equator: "Dominican Republic didn't get gold."

The gold and silver winners lied, but the other three told the truth. How did the event end?

ABCDE = 41523

Define x as true iff the statement made by x is true.

Assume D. Then -E so that D=1, implying -D, a contradiction. We can thus conclude that D is one of the two liars.

Assume -A. Then A finished in fifth place, so A must be a knight; a contradiction. We can conclude that A is a knight and A is either 3 or 4.

Assume B. Then exactly one of C and E must be true, i.e.,  (D=1) = (A>E). (In other words, the parenthesised statements have identical truth values). If D=1 then E must also be a liar, making three liars, which is incorrect. If, OTOH, D>1 and A<E then we would could conclude: C=3, A=4, E=5; so that B is 1 or 2; contradicting the assumption, B. Hence B is a liar.

Recapitulating, we have

• A: A = 1,2,3,4
• B: C <> 3 
• C: E = less than A
• D: E <> 2
• E: D > 1

We can continue

• B,D each < 3
• D <> 1,  so B=1 and D=2
• A = 3 or 4
• C = 4 or 5
• E = 3  so  A = 4  and  C= 5

 

 

 

 

 

 

Posted by FrankM on 2008-05-13 07:27:12