Some hoary old puzzles survive based on their ability to force us into the wrong way of thinking. For instance, consider the classic trip to St. Ives:

“As I was going to St. Ives,
I met a man with seven wives.
Each wife had seven sacks,
Each sack held seven cats,
Each cat had seven kits:
Kits, cats, sacks, and wives,
How many were going to St. Ives?”

The first time I heard this one, I was well into finding powers of seven when something at the back of my mind said, “You’ve been had.” When you listen to the puzzle, the answer is obviously one. As a side note, I’ve never looked up St. Ives and have no idea why anyone would go there.

What is there about this puzzle that has allowed it to survive? I’ve found other puzzles that were cast in the form of poems, and they do not seem to be as popular. Perhaps the answer is that we like to be fooled. On casual hearing, we are led astray into thinking it is a messy, but doable, little exercise in accounting. Then we realize that we have been inattentive.

Several of the puzzles and probability puzzles presented here have that characteristic. When I asked the volume of material left in a sphere that has a one-inch hole drilled through its center, many people wrote to say it couldn’t be solved. They had gone down the wrong path. If they had assumed that I was being honest (!) and the puzzle had a solution, then the answer would have been easy for them to find.

The puzzle of choosing which of the Sultan’s daughters to marry starts out by seeming like a nonsense puzzle with no optimum possible, but with a little bit of thought, we saw that the young man could greatly increase his probability of surviving.

So much for puzzles that are designed for amusement, but what about the puzzles of real life? How many times are we presented with situations that require some analysis, and then we go down the wrong road in finding an answer? For instance, how do you decide who to vote for in any election? What is the probability of being harmed in a terrorist attack if you take a vacation in Europe - or in New York? Should you worry about being hit by lightning in a thunderstorm? (Or a totally different puzzle: Should you worry about being hit by lightning in a thunderstorm?)

We all build up an intuitive version of Bayesian decision theory based on life experience. However, without the rigorous application of statistics and probability combined with proper analysis, we all make mistakes in assigning the probability to significant events. Some people even take pride in doing things wrong. Some belief systems have their followers work hard at overcoming logic and ad hoc statistical analysis to accept as facts things that never happened.
But no matter how hard various vested interests work, the great mass of humanity still loves puzzles and plays with them. That love almost always spills over into practical life. In the long run, those puzzles of life that are solvable in principle do get solved. When Watson and Crick published their work on solving the puzzles of DNA, many questions were answered that had bothered common people and philosophers alike for millennia.

How many are going to St. Ives? All of us.

For those who wish to delve further into decision theory without wading through a lot of equations, I have posted a tutorial on elementary decision theory. It shows examples of faulty physicians’ diagnoses (important for those considering surgery) and how to evaluate anti-terrorist activities (important for everyone). That tutorial can be found here.