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Winning the Science Fair



Isaac and Albert were excitedly describing the result of the Third Annual International Science Fair Extravaganza in Sweden. There were three contestants, Louis, Rene, and Johannes. Isaac reported that Louis won the fair, while Rene came in second. Albert, on the other hand, reported that Johannes won the fair, while Louis came in second.
In fact, neither Isaac nor Albert had given a correct report of the results of the science fair. Each of them had given one correct statement and one false statement. What was the actual placing of the three contestants?
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There are eight possible outcomes: call them a b c ... f

a b c d e f

Louis 1 1 2 2 3 3

Rene 2 3 1 3 1 2

Johannes 3 2 3 1 2 1

We need a case in which Isaac and Albert each gave both a true and false statement

a b c d e f

Isaac: L=1 o o x x x x

R=2 o x x x x o

Albert: J=1 x x x o x o

L=2 x x o o x x

Case f works: Johannes placed first; Renee placed second.

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