Now I've always had a knack for reading people, but this always helps me the morning after when in comes to reading minds. I suggest that this spell be used by someone who already has already evolved their telepathy. Do this spell before going t... Read more of Telepathy at White Magic.caInformational Site Network Informational
Privacy
Home Top Rated Puzzles Most Viewed Puzzles All Puzzle Questions Random Puzzle Question Search


THE BOARD IN COMPARTMENTS.





(The Guarded Chessboard)
We cannot divide the ordinary chessboard into four equal square
compartments, and describe a complete tour, or even path, in each
compartment. But we may divide it into four compartments, as in the
illustration, two containing each twenty squares, and the other two each
twelve squares, and so obtain an interesting puzzle. You are asked to
describe a complete re-entrant tour on this board, starting where you
like, but visiting every square in each successive compartment before
passing into another one, and making the final leap back to the square
from which the knight set out. It is not difficult, but will be found
very entertaining and not uninstructive.
Whether a re-entrant "tour" or a complete knight's "path" is possible or
not on a rectangular board of given dimensions depends not only on its
dimensions, but also on its shape. A tour is obviously not possible on a
board containing an odd number of cells, such as 5 by 5 or 7 by 7, for
this reason: Every successive leap of the knight must be from a white
square to a black and a black to a white alternately. But if there be an
odd number of cells or squares there must be one more square of one
colour than of the other, therefore the path must begin from a square of
the colour that is in excess, and end on a similar colour, and as a
knight's move from one colour to a similar colour is impossible the
path cannot be re-entrant. But a perfect tour may be made on a
rectangular board of any dimensions provided the number of squares be
even, and that the number of squares on one side be not less than 6 and
on the other not less than 5. In other words, the smallest rectangular
board on which a re-entrant tour is possible is one that is 6 by 5.
A complete knight's path (not re-entrant) over all the squares of a
board is never possible if there be only two squares on one side; nor is
it possible on a square board of smaller dimensions than 5 by 5. So that
on a board 4 by 4 we can neither describe a knight's tour nor a complete
knight's path; we must leave one square unvisited. Yet on a board 4 by 3
(containing four squares fewer) a complete path may be described in
sixteen different ways. It may interest the reader to discover all
these. Every path that starts from and ends at different squares is here
counted as a different solution, and even reverse routes are called
different.


Read Answer





Next: THE FOUR KNIGHTS' TOURS.

Previous: THE FOUR KANGAROOS.



Add to Informational Site Network
Report
Privacy
ADD TO EBOOK




Random Questions

The Gentle Art Of Stamp-licking.
Chessboard Problems
The Victoria Cross Puzzle.
Moving Counter Problem
The Milkmaid Puzzle.
Patchwork Puzzles
Drawing Her Pension.
Money Puzzles
The Ploughman's Puzzle
CANTERBURY PUZZLES
On The Ramsgate Sands
MISCELLANEOUS PUZZLES
The Christmas Pudding.
Various Dissection Puzzles
The Three Teacups
THE SQUIRE'S CHRISTMAS PUZZLE PARTY
A Juvenile Puzzle.
Unicursal and Route Problems
The Antiquary's Chain.
Combination and Group Problems
The Thirty-six Letter-blocks.
Chessboard Problems
Bishops--unguarded.
Chessboard Problems
Ovid's Game
MISCELLANEOUS PUZZLES
The Fifteen Orchards
MISCELLANEOUS PUZZLES
The Railway Station Clock.
Money Puzzles