VIEW THE MOBILE VERSION of www.mathpuzzle.ca Informational Site Network Informational
Privacy
Home Top Rated Puzzles Most Viewed Puzzles All Puzzle Questions Random Puzzle Question Search


The Man Of Law's Puzzle

(CANTERBURY PUZZLES)

The Sergeant of the Law was "full rich of excellence. Discreet he was, and of great reverence." He was a very busy man, but, like many of us to-day, "he seemed busier than he was." He was talking one evening of prisons and prisoners, and at length made the following remarks: "And that which I have been saying doth forsooth call to my mind that this morn I bethought me of a riddle that I will now put forth." He then produced a slip of vellum, on which was drawn the curious plan that is now given. "Here," saith he, "be nine dungeons, with a prisoner in every dungeon save one, which is empty. These prisoners be numbered in order, 7, 5, 6, 8, 2, 1, 4, 3, and I desire to know how they can, in as few moves as possible, put themselves in the order 1, 2, 3, 4, 5, 6, 7, 8. One prisoner may move at a time along the passage to the dungeon that doth happen to be empty, but never, on pain of death, may two men be in any dungeon at the same time. How may it be done?" If the reader makes a rough plan on a sheet of paper and uses numbered counters, he will find it an interesting pastime to arrange the prisoners in the fewest possible moves. As there is never more than one vacant dungeon at a time to be moved into, the moves may be recorded in this simple way: 3—2—1—6, and so on.










Answer:


The fewest possible moves for getting the prisoners into their dungeons in the required numerical order are twenty-six. The men move in the following order:—1, 2, 3, 1, 2, 6, 5, 3, 1, 2, 6, 5, 3, 1, 2, 4, 8, 7, 1, 2, 4, 8, 7, 4, 5, 6. As there are never more than one vacant dungeon to be moved into, there can be no ambiguity in the notation.





The diagram may be simplified by my "buttons and string" method, fully explained in A. in M., p. 230. It then takes one of the simple forms of A or B, and the solution is much easier. In A we use counters; in B we can employ rooks on a corner of a chessboard. In both cases we have to get the order





in the fewest possible moves.



See also solution to No. .















Random Questions

Hannah's Puzzle.
Unicursal and Route Problems
The Honeycomb Puzzle.
Unicursal and Route Problems
The Coinage Puzzle
THE PROFESSOR'S PUZZLES
The Peal Of Bells.
Combination and Group Problems
Those Fifteen Sheep.
Combination and Group Problems
The Four Frogs.
The Guarded Chessboard
St. George's Banner.
Patchwork Puzzles
King Arthur's Knights.
Combination and Group Problems
The Star Puzzle.
The Guarded Chessboard
The Barrel Of Beer.
Money Puzzles
The Four Porkers
MISCELLANEOUS PUZZLES
Painting The Die.
Combination and Group Problems
The Round Table
MISCELLANEOUS PUZZLES
The Five Crescents Of Byzantium.
Chessboard Problems
The Victoria Cross Puzzle.
Moving Counter Problem