$1-$ Draw the tree for game nim and compute value of nodes from leaf nodes to root. Assume root $($min$)$ starts with $6$ tokens. As you know, in game nim, at each move, the player must divide a pile of tokens into two nonempty piles of different sizes and if the player in its turn cannot make a move loses the game.

$2-$ In the following tree assume root is MIN, apply minimax and compute root value:

See attached file. Q$2-$Q$3$ Pictures.pdf

$3-$ Use the following move and path definitions in a production system for the knight$$s tour in a $3$ by $3$ board. See attached file.

$1-$ move$(1,8).2-$ move$(1,6).3-$ move$(2,7).4-$ move$(2,9).$

$5-$ move$(3,4).6-$ move$(3,8).7-$ move$(4,9).8-$ move$(4,3).$

$9-$ move$(6,1).10-$ move$(6,7).11-$ move$(7,2).12-$ move$(7,6).$

$13-$ move$(8,3).14-$ move$(8,1).15-$ move$(9,2).16-$ move$(9,4).$

$$ X path$($X$,$ X$).$

$$ X$,$ Y path$($X$,$ Y$)->$ Z $[$move$($X$,$ Z$)$ path$($Z$,$ Y$)].$

Trace it for path$(3,6),$ and for conflict resolution, select the first rule that does not cause the search to loop. a$)$ Use forward chaining $($data driven, bottom$-$up$)$ resolution: b$)$ Using backward chaining $($goal driven, top$-$down$)$ resolution:

$4-$ Given the following horn clauses:

$\%\%$ body mass index example for weight in pound and height in inch:

weight$($tom$,160).$ weight$($jerry$,170).$ weight$($kelly$,180).$

height$($tom$,60).$ height$($jerry$,65).$ height$($kelly$,70).$

bmi$($X$,$ Y$)$ :$-$ height$($X$,$ H$),$ weight$($X$,$ W$),$ Y is W $*703/($H $*$ H$).$

a$)(15$ Pts$)$ What are the possible answers to query: bmi$($X$,$ Y$)?$

b$)(05$ Pts$)$ What are the possible answers to query: bmi$($tom$,$ Y$)?$

$5-$ Briefly explain and write an example:

a$)$ Depth first search

b$)$ Breadth first search

c$)$ Best first search

d$)$ Headed and headless horn clause.Picture for question $2,$

Picture for question $3,$

$\backslash$table$[[1,2,3],[4,5,6],[7,8,9]]$