N squares, each square has 4 sides, that is, 4n matches, and every two adjacent matches are repeated. It should be easy to see that a * * * repeats n- 1 match.
therefore
4n
-
(n- 1)
=
3n+ 1 match.
This method can be used for repeated matching.
Induction, a square, not repeated;
Two squares, repeat1;
Three squares, repeat 2;
Four squares, repeat 3;
……
N squares, repeat n- 1.