Matchsticks Puzzle

The outer $4 \times 4$ square requires one matchstick to be removed. This matchstick has to be from the outer border, which can only break one $1 \times 1$ square.

We have 15 $1 \times 1$ squares remaining. Each time we remove a matchstick, we can only destroy two of them. Thus we need at least 8 more matchsticks removed, for a total of $\boxed{9}$ . This is enough:

(Rewrote the solution to use Challenge Master's suggestions. As has been pointed out, the first version of this solution had a faulty example. Here's a fixed version.)

I found 9 on my own and it happens to be the same image as question master posted. (the above picture is created using MSpaint only)

Anyway , for those who wondering how to get 9 , i decided to do a step by step reasoning. (every step has a meaning to it)

step 1 & 2 : we need to generate as much rectangle as possible , therefore step 1 & 2 makes it the fastest way.

STEP 3 : However in order to generate more rectangle we must avoid the scenario on the right side , as you can see the blue line becomes 2 x 2 square , if you attempted it yourself , i am sure you will be annoyed by one of the 2 blue lines.

Therefore step 3 is locked in the middle.

STEP 4 : having a twin 1 x 1 square on top and bottom after doing step 3 , its obvious that one of them has to become the sole single square. At this point you can choose to remove the outer boundary to eliminate 4x4 square from happening or just ignore it and continue building more RECTANGLE.

STEP 5 : you can only build a rectangle that way , if you do it other way which is removing the boundary just like step 4 , you will end up having a twin 1x1 square which better off to become rectangle in other way round.

STEP 6 & 7 : once you reach step 5 , you will notice that no matter what , the red line in between 6 & 7 CANNOT BE REMOVED. leaving you no choice but to go for step 6 & 7. (you can try and remove that red line after step 5 , i believe you will undo that action very soon)

step 8 and 9 should be obvious , try it yourself and end of explanation.

you can always refer back the picture above from question master for the remaining 2 stick

simple solution, use logic guess...... ..

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LOL

Easiest Method!

Remove 4 vertical sticks in column 2

Remove 4 vertical sticks in column 4

Break the big square by removing 1 from the perimeter

By definition all remaining enclosed spaces are RECTANGLE not square

Remove all sticks frm 2nd and 4th row or 2nd and 4th column and remove 1 stick frm outside border

On dividing the above figure in half we get two rectangles of 2×4 (outer ones) on removing the 4 centre matchsticks for each rectangle(i.e.8 in total)will lead us to a figure having only recctangles(which are obviously not squares) but still we have one square left that is the bigger one 4×4 square and hence we have to remove one more match stick from the boundary of the 4×4 which would leads us to the desired answers.