This morning something interesting was demonstrated on the NPR puzzle with Will Shortz.  Each week a puzzle is given and listeners are given a week to email their answers.  Among those with the correct answer a listener is selected at random to solve a series of puzzle lives on the air the next week.

Last week’s qualifying puzzle was unusually difficult.  There was an exceptionally small number of correct answers.  The best puzzle solvers right?  The listener selected from this group played on the air this morning.  The on-air puzzle was a relatively easy format and on a typical week the guest would get nearly all of them right.  However, today’s winner got fewer than 1/4 of them.  Why?

There are people who are relatively good at getting ideas quickly and there are people whose comparative advantage is in thinking hard for a longer period of time to solve harder puzzles.  In chess, there are players who are good at 5 minute “blitz” time controls and those that are good at chess by mail.  There is little overlap between these groups.  When the qualifying puzzle is easy both types solve the puzzle.  When the qualifying puzzle is hard we get a disproportionately large selection of the postalites.  This means that the randomly selected listener is less likely to do well at the on-air puzzle which favors blitzers over postalites.

The data are available.  Anybody?