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 fulfills 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.
Solutions: 1
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