a$.$ The robot actually begins in square $N,$ facing Up $($but does not yet know it$).$

Based on its limited sensors$,$ how many possibilities are there for its initial

position and orientation, consistent with what it currently perceives?

b$.$ The robot then moves through the squares in this order: $K,F,G,H,$I,$L,O,T.$

How many possibilities are there, at each step, for its position and

orientation, consistent with its entire sequence of observations? At what

point does it know its location with $($effective$)$ certainty?

Soultion attached, can you explain the solutions in greater details and help me understand