Search Problem Formulation

In this question, you need to help our friend Bender from Futurama find his way to the pile of

money. Bender moves in a rectangular maze$-$like environment with dimensions $56,$ as shown in the

figure below. At each time step, Bender can move into an adjacent square if that square is free.

However, this is an unfriendly world in the year $3000$ with hypnotoads that freeze you forever. If Bender is

in the same square as a hypnotoad the game is over.

We know that there exist $3$ hypnotoads and $1$ pile of money in the world but their place is not known.

Which of the following is a minimal correct state space representation?

An integer d denoting the Manhattan distance of Bender to the pile of money.

This problem cannot be represented as a search problem.

One two$-$ple $(x,y)$ encoding the coordinates of Bender, three triples

$(x_1,y_1,d_1),(x_2,y_2,d_2),$ and $(x_3,y_3,d_3)$

encoding the coordinates of the hypnotoads and Bender's Manhattan distance from them and one

triple $(x,y,d)$ encoding the coordinates of the money and Bender's Manhattan distance from it$.$

One tuple $(x,y)$ encoding the coordinates of Bender, three tuples

$(x_1,y_1),(x_2,y_2),$ and $(x_3,y_3)$ encoding the coordinates of the hypnotoads and one tuple $(x,y)$

encoding the coordinates of the pile of money.