Henry Ernest Dudeney/Modern Puzzles/128 - Lines and Squares/Solution

by : $128$

 * Lines and Squares

Solution
We use $15$ straight lines as follows:


 * Dudeney-Modern-Puzzles-128-solution.png

There are:
 * $40$ squares with sides of length $AB$
 * $28$ squares with sides of length $AC$
 * $18$ squares with sides of length $AD$
 * $10$ squares with sides of length $AE$
 * $4$ squares with sides of length $AF$

making $100$ altogether.

We could make as many as $112$ squares with $15$ straight lines, but we were asked for exactly $100$.

With $14$ straight lines we can make only $91$ squares.