The Insurance Act is a most prolific source of entertaining puzzles, particularly entertaining if you happen to be among the exempt.  One’s initiation into the gentle art of stamp-licking suggests the following little poser:  If you have a card divided into sixteen spaces (4 x 4), and are provided with plenty of stamps of the values 1d., 2d., 3d., 4d., and 5d., what is the greatest value that you can stick on the card if the Chancellor of the Exchequer forbids you to place any stamp in a straight line (that is, horizontally, vertically, or diagonally) with another stamp of similar value?  Of course, only one stamp can be affixed in a space.  The reader will probably find, when he sees the solution, that, like the stamps themselves, he is licked He will most likely be twopence short of the maximum.  A friend asked the Post Office how it was to be done; but they sent him to the Customs and Excise officer, who sent him to the Insurance Commissioners, who sent him to an approved society, who profanely sent him—­but no matter.

309.—­THE FORTY-NINE COUNTERS.

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Can you rearrange the above forty-nine counters in a square so that no letter, and also no number, shall be in line with a similar one, vertically, horizontally, or diagonally?  Here I, of course, mean in the lines parallel with the diagonals, in the chessboard sense.

310.—­THE THREE SHEEP.

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A farmer had three sheep and an arrangement of sixteen pens, divided off by hurdles in the manner indicated in the illustration.  In how many different ways could he place those sheep, each in a separate pen, so that every pen should be either occupied or in line (horizontally, vertically, or diagonally) with at least one sheep?  I have given one arrangement that fulfils the conditions.  How many others can you find?  Mere reversals and reflections must not be counted as different.  The reader may regard the sheep as queens.  The problem is then to place the three queens so that every square shall be either occupied or attacked by at least one queen—­in the maximum number of different ways.

311.—­THE FIVE DOGS PUZZLE.

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.

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