On this 5 by 5 grid of dots, one square is shown in the diagram. Including this square, how many different sizes of squares can be formed using four dots of this array as vertices?
+2407 Sadly, I think the best way is to just count.
1 by 1 = 16 squares
2 by 2 = 9 squares
3 by 3 = 4 squares
4 by 4 = 1 square
Note that all the numbers above are squares, this will be a useful pattern when you need to find all the numbers quickly.
1+4+9+16 = 30.
I hope this helped. :))
=^._.^=
+1223 As a general note, for a square array with \(n\) dots on each side, the number of squares is:
\(1^2 + 2^2 + \dots + n^2 = \frac{n(n+1)(2n+1)}{6}\)
+37146 The question asks for the number of different sizes.....not the number of squares
2 x2
3x3
4x4
5x5
four different sizes
+37146 Yes, there are diagonal squares (hence the total squares 55)
and I suppose these 2 x 2 and 3 x 3 squares ARE a different size
so SIX different sizes ya think ?
