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

Puzzles and Curious Problems by Henry Ernest Dudeney: $248$

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.

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.

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Moving Counter Problems: $248$. -- Four in Line
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Combinatorial & Topological Problems: Miscellaneous Combinatorial Puzzles: $455$. Four in Line