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

by : $136$

 * 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.


 * Dudeney-Modern-Puzzles-136.png


 * 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?