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?

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."

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