Four envelopes show 7, A, 2 and H; which must you turn over to test the rule "If the envelope has an A on...
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Problem
Four envelopes show 7, A, 2 and H; which must you turn over to test the
rule "If the envelope has an A on the front then it has an odd number
on the back"?
|-------| |-------| |-------| |-------|
|\ 7 / | | A | |\ 2 / | | H |
|__\/___| |_______| |__\/___| |_______|
" If the envelope has an A on the front then it has an odd number
on the back "
How many envelopes, and which, do you need to turn over to see if the
statement is true?
Show solution
An attempted spoiler: > Assuming the rectangle without the added lines is the front, 2. The A > (to verify the odd number) and the 2 (to verify no A). I've always found this puzzle very amusing. The spoiler just given is the intended answer. However, a few moments' reflection will show that the real answer is: There isn't enough information given. For suppose that the A has an even number on the back. Then you only have to turn over one envelope to see that the statement isn't true! The incorrect answer is *always* the intended one. (This is a famous puzzle, used in psychology experiments.) If the statement *is* true, you have to turn over two envelopes to tell. Maybe a better question would be: How many envelopes, and which, do you need to turn over to see *that* the statement is true? -- Jamie Dreier <pl436000@brownvm.brown.edu> [ Editor: the psychology experiment is the Wason selection task (P. C. Wason, 1966). ]