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 20041118 16:16:32 