Age 7 to 11 Challenge Level:
This solution comes from Henry. Well
To make a square, we need three more matchsticks.
To make a second square, we need three more matchsticks.
I noticed that for each square we make we need three matchsticks,
in addition to the one we had at the beginning. Therefore to make
10 squares we need a total of 31 matchsticks. For 20 squares we
need 61 matchsticks and for 50 squares we need 151.
The general pattern isif $n$ is the number of squares,
we use $3n + 1$ matchsticks in total.