Nim game tree + minimax Problem : Two players have in front of
them a single pile of objects, say a stack of 7 pennies. The first player divides the original
stack into two stacks that must be unequal. Each player alternatively thereafter does the
same to some single stack when it is his turn to play. The game proceeds until each stack has
either just one penny or two—at which point continuation becomes impossible. The player
who first cannot play is the loser. Show, by drawing a game tree, whether any of the players
can always win.

Why is the state 6-1 not going to 3-3-1?If we have 6-1 pennies we can remove 3 pennies from the 6 stack and we have 3-3-1 pennies.So why isn't 3-3-1 not a child of 6-1?
Because - according to the rules above - each player must divide a stack into two stacks that must be unequal.