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At the Olympic Games (6) (Posted on 2004-09-27) Difficulty: 2 of 5
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?

See The Solution Submitted by Federico Kereki    
Rating: 2.6923 (26 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution I get Comment 47 of 47 |

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
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