This blog is primarily about decision theory and how to apply it. But rather than get bogged down in continuous theoretical musings and equations, I try to emphasize the underlying thought processes by adding puzzles which constitute a type of decision making. Since all this ties back to the real world, statistics will often be involved. The difference in decision strategies depending on whether you have a one-time decision or can rely on the statistics of many choices was illustrated in my blog entry More Pain Than Gain.
Developing a taste for puzzles probably happens in adolescence or earlier. I was greatly influenced by Martin Gardener‘s column in Scientific American (see my post on the mechanics of voting). One puzzle from him (this is from memory, so the quote is not exact) goes: You are in a room with some stuff, but no instruments. On a table you find two iron rods. One of them is magnetized. The other is not. How can you determine which is which? The room contains no other ferrous material, batteries, wires, other magnets, etc.
Surprisingly, there are several ways to solve this puzzle.
The charm of this little gem is the “Aha” moment when you see how to do it.
Another puzzle of that genre is the ancient one about drilling a hole through the center of a sphere of ivory (I forget why the sphere was ivory. It just is — but if you know the origin, let me know). The hole is straight and passes squarely through the center. The hole is 1 inch long. What is the volume of ivory left in the drilled sphere?
Yes, I gave you enough information.
Most of my puzzles can be solved with elemental math, but you can use calculus or advance solid geometry to work this one.
Hint: I gave you enough information.
Did you have the “aha” experience?
I will post the answers in a few days.