## THE FIVE DOGS PUZZLE.

(

Chessboard Problems)

In 1863, C.F. de Jaenisch first discussed the "Five Queens Puzzle"--to

place five queens on the chessboard so that every square shall be

attacked or occupied--which was propounded by his friend, a "Mr. de R."

Jaenisch showed that if no queen may attack another there are ninety-one

different ways of placing the five queens, reversals and reflections not

counting as different. If the queens may attack one another, I have

recorded hundreds of ways, but it is not practicable to enumerate them

exactly.

The illustration is supposed to represent an arrangement of sixty-four

kennels. It will be seen that five kennels each contain a dog, and on

further examination it will be seen that every one of the sixty-four

kennels is in a straight line with at least one dog--either

horizontally, vertically, or diagonally. Take any kennel you like, and

you will find that you can draw a straight line to a dog in one or other

of the three ways mentioned. The puzzle is to replace the five dogs and

discover in just how many different ways they may be placed in five

kennels _in a straight row_, so that every kennel shall always be in

line with at least one dog. Reversals and reflections are here counted

as different.

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THE FIVE CRESCENTS OF BYZANTIUM.
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THE THREE SHEEP.