chapter
4 Pages

The Stacked Playing Cards

A problem that has interested many people is the one of the stacked playing cards (or stacked dominoes, or bricks, and so on). If n cards are stacked one on top of the other, how far can the topmost card overhang the bottommost card? The answer, amazingly, is as far as you like provided n is large enough. One solution by Harry Zaremba [1] assumes that the long side of the playing card has length a and that the long edges of the stacked cards lie in the same planes. This simplifies the solution since the narrow sides of the playing cards are of no consequence. Assume that the center of gravity of the top card is 125directly in line with the edge of the card below, as shown in Figure 1, and in general assume that the center of gravity of the top i cards is directly in line with the edge of the (i + 1)th card below. The overhang of the edge of card i with respect to the (i + 1)th card below is a/2i.