move
break the toothpicks and you've doubled your amount of toothpicks
Arrange the 9 toothpicks thus: 7 + 3
Use squares and try it out for yourself. Get a number of squares and make a rectangle 3 squares long by 4 squares wide. Count the squares. You should have 12 squares (or 3*4). That's the best way I know to prove the formula.
3
You make 3-D! Look... 6 squares in one cube and you can do that with toothpicks too!
move
Is this question supposed to have 12 toothpicks to make 4 squares and then move 3 toothpicks to make 3 equal sized squares? Answer depends on the restrictions. Just move 3 sticks from any square to form a straight vertical or horizontal line up of squares is one option if there is no restrictions other than the three resulting squares are equal sizes.
You arrange 12 toothpicks into a large square, subdivided into four squares : 2 toothpicks on each side and four more, one each from the middle of the sides to the center of the large square. Now you have four (small) squares. Take away 2 adjacent toothpicks from the ones in the center, and you have 2 squares : one remaining small one and the large one that has the small one inside it. (see related link)
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Divde
break the toothpicks and you've doubled your amount of toothpicks
Use the image contained below for a reference.
12 toothpics making 4 squares would be: ._ _ |_|_| |_|_| Turning this into 3 squares requires 3 tooth pics to be moved to make (ignore the dots, they're just to line things up!) ._ ...._ |_|_|_| ...|_|
Arrange the 9 toothpicks thus: 7 + 3
Since every square has 4 sides and you only have 10 toothpicks, obviously you can't have the squares be separate. You will need exactly 2 toothpicks to overlap. Once you realize that, there are two shapes that are possible and can be rotated to make a total of 6 different solutions. A straight line (vertical or horizontal): = = = | | | | = = = Or an L-shape (forwards, backwards, and upside-down forwards and backwards): = | | = = | | | = = Sorry that these don't look quite right, the formatting is getting screwed up.
You can make three squares