Operations research (2) - solving puzzles

I posted a little puzzle the other day about four people having to cross a river with a canoe. As an experiment, I also gave the puzzle to a random selection of people at work; everybody gave the 19 minute solution sooner or later. I then asked whether it was possible to find a better solution; some people never answered at all, some said that there was no better solution and three people gave the better solution (one after ten minutes thought, the others after asking other people).

When I originally saw the puzzle, I too came up with the 19 minute answer, but immediately asked myself whether there was a better solution. My thinking went along the following lines 

1. One has to minimise the amount of time, and this can best be done by having the five minute person and the ten minute person cross together.  
2. If those two cross together, someone else has to bring the canoe back (otherwise there'll be a five minute penalty).
3. Thus the two quickest have to cross first; one stays on the far bank whereas the second returns. Then the two slowest cross, then the faster one who stayed on the far bank returns in order to take his companion across.

Or, in terms of how I put the naive solution:  Andrew and Brian cross (2 minutes), Andrew returns (1), Charles and David  cross (10), Brian returns (2), Andrew and Brian cross again (2). This solution requires only 17 minutes, thus saving 10% of the time.

I tried to check the mental processes of the other people; as they almost always started with Andrew and David crossing (10 minutes), they were stuck on the first stage.

What I've noticed with this kind of puzzle (as well as other sorts of ideas) is that the solutions seem easy after the event; the problem is how to make them easy before the event. Of course, if solving a problem were easy, then it wouldn't be a problem by definition.

Although I asked some of the people other puzzles (a tennis racquet and ball together cost $1.10; the racquet costs $1 more than the ball; how much does the ball cost?), almost all of the other puzzles depend on cognitive failure to make them puzzles, where the brain fixes on the wrong part of the question in order to solve the problem (incorrectly). These problems can indeed be solved easily if one thinks slowly and clearly (and if you thought that the tennis ball costs $0.10 then think again). The above is the first question in the Cognitive Reflection Test; the others are

• If it takes five machines five minutes to make five widgets, how long would it take one hundred machines to make one hundred widgets?
• In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake?