Question $1[10$ Points$]$

$($a$)$ Is there a search problem where iterative deepening search is guaranteed to find a solution and breadth first search will fail to find a solution? If yes, give an example. If no$,$ justify.

$($b$)$ Is there a search problem where breadth first search is guaranteed to find a solution and uniform search will fail to find a solution? If yes, give an example. If no$,$ justify.

$($c$)$ Is there a search problem where breadth first search, uniform cost search and iterative deepening search are guaranteed to find the exact same solution? Justify your answer.