Henry Ernest Dudeney/Modern Puzzles/136 - A New Match Puzzle

Modern Puzzles by Henry Ernest Dudeney: $136$

A New Match Puzzle

I have a box of matches.

I find that I can form with them any given pair of these four regular figures, using all the matches every time.

This, if there were eleven matches, I could form with them, as shown, the triangle and pentagon

or the pentagon and hexagon, or the square and triangle (by using only three matches in the triangle);

but could not with eleven matches form the triangle and hexagon,

or the square and pentagon, or the square and hexagon.

Of course there must be the same number of matches in every side of a figure.

Now, what is the smallest number of matches I can have in the box?

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Geometrical Problems: Various Geometrical Puzzles: $136$. -- A New Match Puzzle
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Match Puzzles: $494$. A New Match Puzzle