A building has 16 rooms, arranged in a 4×4 grid. There is a door between every pair of adjacent rooms (“adjacent” meaning north, south, west, and east, but no diagonals). Only the room in the northeast corner has a door that leads out of the building.
In the initial configuration, there is one person in each room. The person in the southwest corner is a psycho killer. The psycho killer has the following traits: If he enters a room where there is another person, he immediately kills that person . But he also cannot stand the site of blood, so he will not enter any room where there is a dead person.
As it happened, from that initial configuration, the psycho killer managed to get out of the building after killing all the other 15 people. What path did he take?
The killer starts by entering the room to the north of his room and killing the person there. Then he comes back to the starting room (This is the only room to which he can come back, because there can’t be any dead body there as it was originally occupied by himself.) Then he proceeds to other rooms in the sequence 2, 3, 4, 8, 7, 6, 10, 9, 13, 14, 15, 11, 12 and 16, exiting from there. (See the figure for room numbers and path taken.)
Added later: He can take an alternate path with first move eastwards (to Room No. 2) and coming back and taking a path mirroring the first solution, along 1 -> 2 -> 1 -> 5 -> 9 -> 13 -> 14 -> 10 -> 6 -> 7 -> 3 -> 4 -> 8 -> 12 -> 11 -> 15 -> 16.
See image for room numbers and the ‘psycho-paths’.
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