In rearranging the Planets, each of the five may be moved once in a straight line, in either of the three directions mentioned.  They will, of course, obscure five other Stars in place of those at present covered.

315.—­THE HAT-PEG PUZZLE.

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.

[Illustration]

316.—­THE AMAZONS.

[Illustration]

This puzzle is based on one by Captain Turton.  Remove three of the queens to other squares so that there shall be eleven squares on the board that are not attacked.  The removal of the three queens need not be by “queen moves.”  You may take them up and place them anywhere.  There is only one solution.

317.—­A PUZZLE WITH PAWNS.

Place two pawns in the middle of the chessboard, one at Q 4 and the other at K 5.  Now, place the remaining fourteen pawns (sixteen in all) so that no three shall be in a straight line in any possible direction.

Note that I purposely do not say queens, because by the words “any possible direction” I go beyond attacks on diagonals.  The pawns must be regarded as mere points in space—­at the centres of the squares.  See dotted lines in the case of No. 300, “The Eight Queens.”

318.—­LION-HUNTING.

[Illustration]

My friend Captain Potham Hall, the renowned hunter of big game, says there is nothing more exhilarating than a brush with a herd—­a pack—­a team—­a flock—­a swarm (it has taken me a full quarter of an hour to recall the right word, but I have it at last)—­a pride of lions.  Why a number of lions are called a “pride,” a number of whales a “school,” and a number of foxes a “skulk” are mysteries of philology into which I will not enter.

Well, the captain says that if a spirited lion crosses your path in the desert it becomes lively, for the lion has generally been looking for the man just as much as the man has sought the king of the forest.  And yet when they meet they always quarrel and fight it out.  A little contemplation of this unfortunate and long-standing feud between two estimable families has led me to figure out a few calculations as to the probability of the man and the lion crossing one another’s path in the jungle.  In all these cases one has to start on certain more or less arbitrary assumptions.  That is why in the above illustration I have thought it necessary to represent the paths in the desert with such rigid regularity.  Though the captain assures me that the tracks of the lions usually run much in this way, I have doubts.