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

Modern Puzzles by Henry Ernest Dudeney: $128$

Lines and Squares

Here is a simple question.

With how few straight lines can you make exactly one hundred squares?

Thus, in the first diagram it will be found that with nine straight lines I have made twenty squares

(twelve with sides of the length $AB$, six with sides $AC$, and two with sides of the length $AD$).

In the second diagram, although I use one more line, I only get seventeen squares.

So, you see, everything depends on how the lines are drawn.

Remember there must be exactly one hundred squares -- neither more nor fewer.

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Geometrical Problems: Various Geometrical Puzzles: $128$. -- Lines and Squares
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Geometrical Problems: Triangle, Square & Other Polygon Puzzles: $259$. Lines and Squares