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There are 9 squares I can see 12 squares in an array of 2 * 4 squares
Well you can look at it like this to help explain: _____ |_|_|_| |_|_|_| |_|_|_| Each small square is 1/9 (one ninth) of the large square. So if you have 3 over 9 (3 ninths) that is 3 small squares. If you have 4 over 9 (4 ninths) that is 4 small squares. 3 small squares is less than 4 small squares, as is 3/9 < 4/9.
1+4+9 = 14 squares.
Infinitely many, but only 30 squares within a 1 unit grid. 4*4 square: 1 3*3 squares: 4 2*2 squares: 9 1*1 squares: 16
In a square with 25 smaller squares arranged in a 5x5 grid, there are a total of 55 squares. This includes the 25 individual smaller squares, the 16 squares formed by combining 4 smaller squares, the 9 squares formed by combining 9 smaller squares, the 4 squares formed by combining 16 smaller squares, and the 1 square formed by combining all 25 smaller squares.