The sliding puzzle game, shown in the following figure, consists of a $33$ board with $8$ numbered tiles and one blank space. At each turn, the agent moves one of adjacent tiles to the blank space. We want to come up with an algorithm to reach the goal state $($on the right in the figure$)$ no matter what the starting state is$.$

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

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

A$.$ What is the size of that state space?

B$.$ Does every board configuration $($e$.$g$.,$ one of them is on the left in the figure$)$ have a unique sequence of moves to reach the goal state?

C$.$ We define two different heuristics: $h_1(n)=$ Total number of misplaced titles, and $h_2(n)=$ Sum of Manhattan distances for each tile to its the goal location. Examine the following heuristics for whether they are admissible only, consistent only, both, or neither.

$h_3(n)=$max$(h_1(n),h_2(n))$

$h_4(n)=$min$(h_1(n),h_2(n))$

Comparing the above four heuristics, which one is $($or are$)$ the best?

The following python script runnning in the CLI $($Command Line Interfacc$)$ environment returns an error when executing $A+B.$ What could be the reason?

print$($list$($A$))$

$\{10,20,30,40,50]$

print$($B$)$

$[\text{'}10\text{'},\text{'}20,\text{'}30\text{'},\text{'}40\text{'},\text{'}50\text{'}]$

$A+B$

Which code$($s$)$ listed in the following would print $11?$