onsider the game nim with the following rules. The game starts with n sticks in a pile. Turns

alternate between players. For each turn, the active player must select a pile and divide it into two

smaller piles. Piles containing only one or two sticks can not be divided further. The last player able

to make a legal move wins. Note, this is one variation of the game, many others exist.

Consider the following path with n $=6.$ MAX is the starting player, then MAX and MIN alternate

actions with MAX winning $($last player able to make a legal move$).$

The following is part of the game tree for n $=6.$

You will examine the game tree for nim with n $=7.$

$4/7$