Freshman Seminar 23j: Chess and Mathematics (Fall 2004)
Supplementary Question

An enumerative chess problem

Consider the following position of the 16 White units
(in algebraic notation, King b5, Queen d1, Rooks b1 and h1, Bishops c1 and f1, Knights c3 and e5, Pawns a2, b2, c4, d2, e2, f3, g3, h2):

1) [This should be easy.] How many moves would it take White to reach this setup from the initial position? Explain.

2) [Not as easy, but you'll know when/if you get the right answer.] How many possible sequences of moves of that minimal length are there that reach this setup? Explain.

3) [Open-ended] Can you construct a similar puzzle that I could use for next year's edition of the Math & Chess seminar? Can you propose any other questions suggested by this puzzle? Can you answer or partially answer some of them?

Please send your replies directly to me by e-mail (elkies@math.harvard.edu -- text only, no HTML or attachments unless absolutely necessary, NO .doc files).