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:
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[[[[Table]]]]]]]

(In reply to re: Solution, spoiler by Charlie)

You actually couldn't extend this as far as you wanted given more decks.  The physical nature of this puzzle, combined with the inability to perfectly place the cards, there would be some limit on how much overhang you could achieve (for example, I find that I can stack only about 250 pennies in a vertical tower before some inconsistency topples them).  You'd have to worry about the roof (or, if theres no roof, then wind might be a problem).  Of course, you'd also need a table of infinite strength to hold the cards in a very high tower, as the weight of the cards is not zero.  Add in that the cards are flexible, and you're then stacking objects of complex geometry (i.e., not flat).

My best guess at perplexian nerve stability (and measuring accuracy) is that the best result we could achieve, with one deck, would probably be no more than 75% of the theoretical best answer, previously supplied.

But I'm getting carried away here...

 

 

Posted by Cory Taylor on 2005-02-04 16:27:24