THE HAT-PEG PUZZLE.
(
Chessboard Problems)
Here is a five-queen puzzle that I gave in a fanciful dress in 1897. As
the queens were there represented as hats on sixty-four pegs, I will
keep to the title, "The Hat-Peg Puzzle." It will be seen that every
square is occupied or attacked. The puzzle is to remove one queen to a
different square so that still every square is occupied or attacked,
then move a second queen under a similar condition, then a third queen,
and finally a fourth queen. After the fourth move every square must be
attacked or occupied, but no queen must then attack another. Of course,
the moves need not be "queen moves;" you can move a queen to any part of
the board.
Answer:
The moves will be made quite clear by a reference to the diagrams, which
show the position on the board after each of the four moves. The darts
indicate the successive removals that have been made. It will be seen
that at every stage all the squares are either attacked or occupied, and
that after the fourth move no queen attacks any other. In the case of
the last move the queen in the top row might also have been moved one
square farther to the left. This is, I believe, the only solution to the
puzzle.
[Illustration: 1]
[Illustration: 2]
[Illustration: 3]
[Illustration: 4]
