[Syzygies]

In the 1960's my dad programmed Jotto (a simpler five letter secret word game) on Kodak's computers. Entropy became the first interesting mathematical concept that I learned.

Log base 2 of the remaining words is a measure of how many yes/no questions it would take to identify the word. An entropy strategy looks for a clue word that minimizes the expected value of this measure. One optimizes sum p log p over the pile sizes.

Pure mathematicians prefer certain concepts with a religious fervor. Often this has been informed by a reasonable number of problems where a concept has been proven optimal. The best applied mathematicians understand pure math but prefer practical work. To a pure mathematician, the rest are just guessing.

Here, one needs a clearly stated objective function for measuring success. Entropy strategies are often optimal for simple objective functions.

A critical detail for this game: The secret words come from a shorter list than the valid guess words. One wants a guess word that best partitions the shorter list of secret word candidates, not the full list of valid guess words.