25. The Branching Factor

Errata: The final upper bound calculation incorrectly shows 12^13; it should be 12^11. There are 25 total moves; 2 are used for the openings (with 25 and 24 choices, respectively), and the last 12 moves are used in the calculation 12! = 5e8. 25 - 2 - 12 = 11 moves unaccounted for with an average branching factor of 12. The calculation 25 x 24 x 12^11 x 5e8 more closely matches the total estimate shown as 3e23.