Henry Ernest Dudeney/Puzzles and Curious Problems/248 - Four in Line

by : $248$

 * Four in Line
 * Here we have a board of $36$ squares, and four counters are so placed in a straight line
 * that every square of the board is in line horizontally, vertically, or diagonally with at least one counter.
 * In other words, if you regard them as chess queens, every square on the board is attacked by at least one queen.


 * Dudeney-Puzzles-and-Curious-Problems-248.png


 * The puzzle is to find in how many different ways the four counters may be placed in a straight line so that every square shall thus be in line with a counter.
 * Every arrangement in which the counters occupy a different set of four squares is a different arrangement.
 * Thus, in the case of the example given, they can be moved to the next column to the right with equal effect,
 * or they may be transferred to either of the two central rows of the board.
 * This arrangement, therefore, produces $4$ solutions by what we call reversals or reflections of the board.
 * Remember that the counters must always be disposed in a straight line.


 * It will be found an entertaining little puzzle.