is to
define, a child can learn it by inspection in a few minutes.

I have shown in the diagram how twelve knights (the fewest possible that
will perform the feat) may be placed on the chessboard so that every
square is either occupied or attacked by a knight. Examine every square
in turn, and you will find that this is so. Now, the puzzle in this case
is to discover what is the smallest possible number of knights that is
required in order that every square shall be either occupied or
attacked, and every knight protected by another knight. And how would
you arrange them? It will be found that of the twelve shown in the
diagram only four are thus protected by being a knight's move from
another knight.

THE GUARDED CHESSBOARD.

On an ordinary chessboard, 8 by 8, every square can be guarded--that is,
either occupied or attacked--by 5 queens, the fewest possible. There are
exactly 91 fundamentally different arrangements in which no queen
attacks another queen. If every queen must attack (or be protected by)
another queen, there are at fewest 41 arrangements, and I have recorded
some 150 ways in which some of the queens are attacked and some not, but
this last case is very difficult to enumerate exactly.

On an ordinary chessboard every square can be guarded by 8 rooks (the
fewest possible) in 40,320 ways, if no rook may attack another rook, but
it is not known how many of these are fundamentally different. (See
solution to No. 295, "The Eight Rooks.") I have not enumerated the ways
in which every rook shall be protected by another rook.

On an ordinary chessboard every square can be guarded by 8 bishops (the
fewest possible), if no bishop may attack another bishop. Ten bishops
are necessary if every bishop is to be protected. (See Nos. 297 and 298,
"Bishops unguarded" and "Bishops guarded.")

On an ordinary chessboard every square can be guarded by 12 knights if
all but 4 are unprotected. But if every knight must be protected, 14 are
necessary. (See No. 319, "The Knight-Guards.")

Dealing with the queen on n squared boards generally, where n is less
than 8, the following results will be of interest:--

1 queen guards 2 squared board in 1 fundamental way.

1 queen guards 3 squared board in 1 fundamental way.

2 queens guard 4 squared board in 3 fundamental ways (protected).

3 queens guard 4 squared board in 2 fundamental ways (not protected).

3 queens guard 5 squared board in 37 fundamental ways (protecte