Henry Ernest Dudeney/Puzzles and Curious Problems/247 - The Counter Cross

by : $247$

 * The Counter Cross
 * Arrange twenty counters in the form of a cross, in the manner shown in the diagram.


 * Dudeney-Puzzles-and-Curious-Problems-247.png


 * Now, in how many different ways can you point out four counters that will form a perfect square if considered alone?
 * Thus the four counters composing each arm of the cross, and also the four in the centre, form squares.
 * Squares are also formed by the four counters marked $\text A$, the four marked $\text B$, and so on.


 * And in how many ways can you remove six counters so that not a single square can be so indicated from those that remain?