My father liked "brain teasers" (although Mum inclined to Molly Strait's
opinion). Here's one of his -- it comes in a not-so-difficult and a very
difficult
version:
12 coins: They are identical in appearance, but one is counterfeit, being
heavier than the others. You have a simple 2-pan balance. (If students
don't know what that is, they may know it as the "scales of justice" held
by the blindfolded statue.) Show that you can always detect the fake coin
in three comparisons using the balance. (If you like, you can give hints
about how many coins to put on each pan of the balance for the first
weighing -- 6 vs. 6? 4 vs 4?)
Hard version: (Took me many many tries -- Dad never believed in giving
away the answers, so I won't either, but it is solvable without any "tricks.")
Same as above, but the counterfeit coin is either heavier or lighter than
the rest, and you don't know which. Still only 3 comparisons with the balance.
-David
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David G. Likely, Department of Psychology,
University of New Brunswick
Fredericton, N. B., E3B 5A3 Canada
History of Psychology:
http://www.unb.ca/web/psychology/likely/psyc4053.htm
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