The 4 Card Test
This is a famous problem in the study of deductive reasoning and logic.
You are shown a set of four cards placed on a table, each of which has a number on one side and a colored patch on the other side.
The visible faces of the cards show 3, 8, red and brown.
Which card(s) must you turn over in order to test the truth of the proposition that if a card shows an even number on one face, then its opposite face is red?
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The cards we need to flip over are 8 and brown. Consider each card.
–Flip over 3? If we see the color red, that does not break the rule. The rule says every card with an even number has the color red on the other side. We could certainly have cards with red on one side and an odd number on the other side without breaking the rule. No need to flip it.
–Flip over 8? If the rule is true, this card better have red on the other side. Must flip it.
–Flip over red? The rule states what the opposite side of cards showing an even number is. If we flip over the red card to find an odd number, that does not break the rule. No need to flip it.
–Flip over brown? If we flip this card over and find an even number, then that would break the rule. For that would be an example of a card with an even number that has brown on the other side, not red. Hence we must flip this card over.