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:
(In reply to Solution, spoiler
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