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Math problems in Grade One Volume 1 20 16
Here I write a different idea from the above:

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.