One of the wonderful things about having ancestors is that we can learn from them. As John McLoughlin observed in Toolmaker Koan, this allows us a Lamarckian cultural evolution: acquired traits can now be passed on.

"A human being, producing an invention, passes that invention on to the next generation via the route of what we call culture. This I [the crazy alien artifact speaking] would call the Lamarckian 'genetic apparatus'. As you can plainly see from your own history, cultural--Lamarckian--evolution is far faster than Darwinian evolution...."

And a good thing, too. F'rinstance, thanks to my father's attempt to flirt with my mother with word problems ("two trains are headed for each other at different speeds...."), which ended in literal tears and curses, I know that I ought not to share the particularly pleasant problems I encounter with my wife.

But this conclusion is unsatisfying, since I really do like word problems. So I bethought me of the Internet, which I have never made cry, despite my best efforts. Both are from the Lilavati of Bhaskara, which was named for the mathematician's daughter. He had determined the only propitious moment for her marriage, and the girl, anxiously watching the clepsydra, let fall an unnoticed pearl from her finery which stopped the clock. The hour passed before this accident was learned of, and in consolation the mathematician named his treatise after her. Which I'm sure made everything all better.

Both are fairly simple problems, one determinate, the other in-. What I like is not the intricacy of reasoning necessary, but the clean, wholesome, five-finger exercise.

1. A bamboo 32 cubits high breaks in the wind, and the tip hits the ground 16 cubit away from the base. At what height from the ground did it break?

2. A peacock is perched on a pillar. At the base of the pillar is a snake's burrow. Spotting a serpent at a distance from its burrow equal to three times the height of the pillar, the peacock pounced precipitously in a straight line as the serpent slithered for safety. If both the peacock and its prey traveled the same distance before the messy end of the snake, how far from the pillar did they meet?

Lo! I hope no one over the age of twelve has been reduced to tears. Comments are open, but since these are rather simple problems, I would prefer to save them for questions or criticism rather than the answers themselves.

Grâce à Mr. Boyer's A History of Mathematics.