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Teetering on the Edge (Posted on 2005-02-04) Difficulty: 3 of 5
A deck of 52 playing cards is placed over-hanging the straight edge of a table. The cards are identical and uniformly dense. Suppose these cards are 3.5 inches in length, and this side is perpendicular to the table's edge. If the individual cards can be pushed forward or pulled back from the edge as you please, what is the farthest the cards can reach beyond the edge without any card tipping or leaning off of the card or table immediately below it?

Example of what a three-card deck may look like:
               -----------
          -----------
           -----------
[[[[Table]]]]]]]

See The Solution Submitted by owl    
Rating: 4.0000 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Solution, spoiler | Comment 2 of 8 |
(In reply to Solution, spoiler by Hugo)

Since this is half the sum of the harmonic series extended out to 52 terms, if you were not limited to one deck, you can make the overhang as large as you want by adding extra decks, as the harmonic series does not converge.

Of course in the puzzle, we're limited to one deck of 52.


  Posted by Charlie on 2005-02-04 15:36:22
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