Given the layout of $17$ sticks $($forming $6$ squares$)$ shown in the figure, you are

required to remove exactly $5$ sticks in such a way that the remaining configuration

forms exactly $3$ squares. How many states exist if we form the problem with the

following two operators respectively?

i$)$ Operator A: remove five sticks at a time.

ii$)$ Operator B: remove three squares at a time. d$.$ Given the layout of $17$ sticks $($forming $6$ squares$)$ shown in the figure, you are

required to remove exactly $5$ sticks in such a way that the remaining configuration

forms exactly $3$ squares. How many states exist if we form the problem with the

following two operators respectively?

i$)$ Operator A: remove five sticks at a time.

ii$)$ Operator B: remove three squares at a time.