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 At the Olympic Games (6) (Posted on 2004-09-27)
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."
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)

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 Solution | Comment 41 of 47 |

Argentine: "I was not last."
Dominican Republic: "Equator got silver."
Equator: "Dominican Republic didn't get gold."

Suppose A lies -> the first sentence would become "I was last", but for A to lie would mean it must be on 1st, or 2nd place, so we got a contradiction     (A is last but takes gold or silver(?!)). Because of that A can't lie(a).

Suppose D tells the truth->E has silver->E lies.

If E lies then the last sentence becomes "D did get the gold", but we supposed D told the truth, so we have another contradiction and that means that D didn't tell the truth.So D lies(b)

Because (b) the fourth sentence becomes "E didn't get silver".

So, E must have taken gold(c1) or "one of the last 3 places"(c2)

If E took gold ->E lies ->D took gold (and that is  an obvious contradiction), so E didn't take the gold for sure->(c1) is false.

if (c1) false->(c2) must be true, and even more E tells the truth, so the last sentence is true(d)

Using (d) and (b) the only possibility is that D took silver.(e)

Untill now we know that D lies and A,E don't.

So, we must find whether B or  C lies.(f)

We suppose B tells the truth ->Canada took bronze so ,C can't lie, but from (f) C or B must lie, and because of that our supposing is false, and so B lies (Occam's Blade).(g)

From (g),(e)->B took gold.

For A,E,C there are only 3,4,5 places left to fill.

B lies so C didn't take bronze, and that means C is on 4th or 5th place.But because "A ended behind E" and "A isn't last" the only possibility is Canada on 5th, A on 4th  and E on 3rd place.

1.B

2.D

3.E

4.A

5.C

 Posted by cezar on 2004-11-18 16:16:32

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