# Show this man the exit, enter into cell only once and should cover all cells

Show this man the exit

Conditions :

1. should cover all cells
2. should not enter the cell twice (only once)

There is a trick to this.

He is only allowed to enter each cell once during the solution. You could interpret this to mean that he can still enter his starting cell once after he has exited it.

With that interpretation, the solution is easy.

Exit the starting cell, immediately enter it, and then visit all the other rooms. For example like this:

 2  1  6  7
3  4  5  8
12 11 10  9
13 14 15 16

Without this trick

it is impossible as JMP's answer proves.

• It just says "Show him the exit", not to exit. – user118161 Apr 6 at 1:55

It's

Impossible

because

Imagine the room is like a chess board. The bloke starts on a black square. He moves from a black square to a white square, and vice versa. There are $$8$$ white squares and $$7$$ black squares left to cover, therefore he will end on a white square in order to cover all rooms - but he needs to be on a black square to exit.

• Also rot13(Oevqtrf bs Xbavtforet) idea. – stuart stevenson Apr 6 at 16:15

I think the solution is:

that you only have to show him the exit, so it is enough to pass by the exit while running through to cover all cells. So the solution is go down 3, 1 right, 3 up, 1 right, 3 down, 1 right, 3 up.