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?
(In reply to
Problem Solution by K Sengupta)
(I) Assume that the Argentinian got the gold. Then his statement that he wasn't last was true. This is a contradiction.
Assume that the Canadian got the gold. Then it follows that, the Brazilian spoke falsely, so he must have got the silver. The Dominican's statement that Equator got silver is false. So, the Dominican who didn't get a gold or silver spoke falsely. This is a contradiction. So, the Canadian did NOT get the gold.
Assume that the Equatorian got gold. Then his statement that the Dominican didn't get gold is true. This is a contradiction.
Similarly, if the Dominican got gold then by his false statement the Equatorian didn't get silver. Thus, the Equatorian spoke the truth saying that the Dominican didn't get the gold. This is a contradiction.
Accordingly, the only possibility is that, the remaining individual - that is, the Brazilian - GOT the GOLD.
(II) Assume that the Argentinian got the silver. Then, his statement that he wasn't the last is true. This is a contradiction.
Assume that the Canadian got the silver. Then, the Dominican's statement is false. So the Dominican also won the silver. This is a contradiction.
Assume that the Equatorian got silver. Then his false statement implies that the Dominican got the gold. But, we have established before that the Brazilian got the gold. This leads to a contradiction.
Accordingly, the remaining individual -- that is, the Dominican GOT the SILVER.
(III) None of these these three individuals: The Argentinian, the Canadian and the Equatorian got the gold or the silver. Therefore, each of their statements must be true.
In terms of true statements made by the Argentinian and the Canadian:
Argentina ended up behind Equator but, Argentina wasn't last (fifth position).
Since the Brazilian got the gold and the Dominican got the silver, the only possibility is: (Equator, Argentina) = (3,4), so that the Equatorian got the bronze and the Argentinian assumed the fourth position.
Accordingly, the remaining individual, that Is, the Canadian came last (fifth position).
Consequently , each country's position is depicted in terms of the under noted chart as follows:
Position Country
-------------- ------------
Gold (First) Brazil
Silver (Second) Dominican Republic
Bronze (Third) Equator
Fourth Argentina
Fifth Canada
Edited on July 21, 2022, 5:56 pm
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