Three square napkins and a square table problem
You have 3 square napkins (one square foot each).
What's the area of the largest square table you can cover
with the 3 napkins?
Please, give me the way to solve it, not only the solution.
Thank you. :-)
I don't know of any "methods" for solving puzzles like this. I had to
have 3 "Aha!"s (sudden insights) before I came up with a configuration
for the napkins that will cover the largest square table. Try this:
how would you arrange the napkins (imagine sewing their edges together
where they meet) so they cover the largest ROUND table. (I just love
symmetry.) I propose that the same configuration will cover the largest
square table. The answer I get for the DIAGONAL of the table is:
1 + ( sqrt(2) ) / 2 [the form of the answer is, in itself, a hint]
For more information about puzzles like this and how to solve them, read
"Aha! Insight" by Martin Gardner, Scientific American, Inc., 1978
Correction: the diagonal is just 3/2, and if you write it
as 1 + 1/2, then the form of the answer is, indeed, a big hint.
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Update: June 2012