This applet simulates the pouring of water into a triangular stack
of buckets. When a bucket is full, it spills its excess water equally
out its left and right sides. The result is something like Pascal's
Triangle, but more complicated since buckets only spill once they
are full. The applet was inspired by a question from my step-cousin's
high school math class: how much water must be poured before the sixth
row is "one-full", i.e. at least one bucket on the sixth row is full?
(Computing this analytically is harder than it sounds; try it! The answer
turns out to be precisely 15.4. Actually the high school question uses
two-litre buckets for some reason, thus doubling the answer to 30.8.)
An easier question is, how much water is required before the n'th row
is *completely* full (answer: 2^n - 1).

The applet accepts the following keyboard inputs. (You may need to "click" on the applet first.)

- Press 'p' to pause/unpause the simulation.
- Press 'r' to restart.
- Press 'f' and 's' to make the water flow faster or slower.

Applet by Jeffrey S. Rosenthal. [Return to my Applets Page / Home Page]