[jxrlppkn] most defenses

consider a mate in N chess problem.  how many paths through the game tree end in checkmate in exactly N moves?  (also consider less than N moves.)

for a good chess problem with no duals, every attacker move in that subset of the game tree has exactly one move that accomplishes mate in N.  if not, specify a strategy (e.g., fewest defender branches) that deterministically picks one attacker move and prune the rest of the attacker branches.  only alternatives by the defender contribute to the total branches.

compose chess problems that maximize the number of paths.  or the number of nodes in the pruned game graph (branches may merge through transposition).

such problems tend to be annoying for humans to solve, needing to check many cases.