That museum has 46 rooms linked by corridors.
In some rooms (A, B, C, D, E) precious jewels are guarded day and night.
At evenings, the chief of the guards patrols, passing through each room and closing the doors.
He starts and ends his turn at the guards room P.
He locks a guard in each of the A, B, C, D and E rooms for the night.
These guards have no key and say to the guards room by radio that all is right, as soon as they are locked in.
On the morning, the guard D is found knocked down and the jewel has vanished.
The chief guard swears he went only once in every room, that no other guard has a key and everything
was allright when he leaved the guard.
The guards at the guards room confirm that guard D has called by radio and said all was OK after he had been locked in.
Prove that the chief guard is a liar.