Four students Art, Ben, Cal and Don competed in a series of four quiz contests involving English, General knowledge, Logic, and Math. They are now wondering about the outcome.

Art thinks Don won the Logic award.
Ben thinks Cal won the English prize.
Cal thinks Art did not win the Math title.
Don thinks Ben won the General Knowledge trophy. 

As it turns out, both surmises about winners of the English and General Knowledge contests were wrong, and both surmises about the winners of the Math and Logic contests were correct.

Who won which contest?

Don won logic, Art won English, Ben won math and Cal won General Knowledge. Or Don won logic, Art won English, Ben won nothing, and Cal won both Math and General Knowledge.  I assume the problem intent is that each of the students won one and only one contest  If so:

Stmt 1 is true, so Don won Logic
Stmt 2 is false, so Cal did not win English, but then neither did Ben, or why would he think Cal did?
Stmt 3 is true, so Art did not win math, but Cal may have or my not have won it
Stmt 4 is false, so Ben did not win Gen Knowledge, but then logically neither did Don.

if each student is to win one contest and one only, then Ben must have won math.  Then it follows that Cal won General Knowledge and Art English.  However if it is not a requirement that each student win one contest, then the other solution works I think.

Posted by Kenny M on 2013-11-29 11:51:32