Question Tom, Ann and John find themselves trapped in a dark and cold dungeon. A

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Tom, Ann and John find themselves trapped in a dark and cold dungeon. After a quick search the boys find three doors, the first one red, the second one blue , and the third one green.

Behind one of the doors is a path to freedom. Behind the other two doors, however, is a fatal trap. Opening a door to the fatal trap means almost certain death. On each door there is an inscription

(red) : “freedom is not behind this door”

(blue) : “freedom is behind this door”

(green) : “freedom is not behind the red door”

Given the fact that at LEAST ONE of the three statements on the three doors is True and at LEAST ONE of them is False, which door would lead the boys to safety? Justify your answer.

Explanation / Answer

Given fact: Atleast one of the three statement is True, and atleast on of the three statement is False.

So, the possibilities are:

From the above table, we can conclude that, the blue door will lead the boys to safety.

Red Blue Green Comment Conclusion False False True Red, and Green statements lead to contradiction, and blue statement is false. No clarity on freedom leading door. False True False Red, and Blue doors both lead to freedom which is not true. Something wrong as, two doors are trap, and cannot lead to freedom. False True True Red, and Green statements lead to contradiction, so, blue leads to freedom. Blue leads to freedom, while the other two leads to contradiction. True False False Red, and Green statements lead to contradiction, and blue statement is false. No clarity on freedom leading door. True False True All three statements together states that, there is no freedom behind any door. No freedom leading door. True True False Red, and Green statements lead to contradiction, and blue leads to freedom. Blue leads to freedom, while the other two leads to contradiction.

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