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