25
225
The correct answer is 76. There are 9 points in the grid. You can pick any 3 out of these 9 points in 9*8*7/(3*2*1) = 84 ways. However, 3 will form horizontal lines in the grid, 3 will form vertical lines in the grid, and 2 will form diagonal lines in the grid. None of these 8 triplets will form triangles, but all the rest will. So the answer is 84-8=76.
5x5=25 squared 1+2+3+4+5+6+7+8=36 The only way to fit them in would be to fold them XD
Oh, dude, you're really asking me to count squares now? Okay, so in a 5x5 grid, there are 25 individual squares of various sizes. You've got your big squares, your medium squares, your tiny squares... it's a whole square party in there. So, like, 25 squares, man.
25
225
you can make 76 different triangles on a 3x3 grid
5!=5*4*3*2*1
If its a 4 by 5 grid, there are 20 squares because 4 times 5 =20 20 by 2 is 40 so there are 40 triangles because there are 2 triangles that fit into each square. Hope this helps!
9 squares = 18 triangles * * * * * The correct answer is 76. There are 9 points in the grid. You can pick any 3 out of these 9 points in 9*8*7/(3*2*1) = 84 ways. However, 3 will form horizontal lines in the grid, 3 will form vertical lines in the grid, and 2 will form diagonal lines in the grid. None of these 8 triplets will form triangles, but all the rest will. So the answer is 84-8=76.
The correct answer is 76. There are 9 points in the grid. You can pick any 3 out of these 9 points in 9*8*7/(3*2*1) = 84 ways. However, 3 will form horizontal lines in the grid, 3 will form vertical lines in the grid, and 2 will form diagonal lines in the grid. None of these 8 triplets will form triangles, but all the rest will. So the answer is 84-8=76.
30 triangles (1 to the power of 2) + (2^2) + (3^2) + (4^2) = 1 + 4 + 9 + 16 = 30
5x5=25 squared 1+2+3+4+5+6+7+8=36 The only way to fit them in would be to fold them XD
Oh, dude, you're really asking me to count squares now? Okay, so in a 5x5 grid, there are 25 individual squares of various sizes. You've got your big squares, your medium squares, your tiny squares... it's a whole square party in there. So, like, 25 squares, man.
You really should do your own homework - this is a question designed to make you analyse number patterns and devise a method to predict the answer that can be applied to grids of differing size. If we start with a square cut into a 3x3 grid, we can count the nine single (1x1) squares in the grid, the one 3x3 square, and then four 2x2* squares, making a total of 14. Try it out, then work your way up to 6x6 (a 36 square grid) by way of 4x4 and 5x5, looking to see how the grid's dimensions correlate to the number of varying-sized squares that can be counted. As a tip- in a 6x6 grid, you will have one 6x6 square, thirty-six 1x1 squares, and how many 2x2, 3x3, 4x4, and 5x5 squares? *The squares can overlap, obviously.
If you have a grid of 5x5 squares you will have no triangles at all since there are no diagonal lines. * * * * * Here is a more likely answer - though I am not sure it is totally correct. A triangle is defined by three vertices. The total number of ways of picking 3 out of 25 points is 25*24*23/(3*2*1) 25 ways of picking a point from the grid at random, 24 ways to pick another point from the grid and 23 to pick the third. Divide by 3*2*1 since the order in which these collinear points is picked does not matter. However, some of these are not triangles: they are not triangles if all three points are in the same row or in the same column. Number of ways for that = 2*(25*4*3)/(3*2*1) 25 ways of picking a point from the grid at random, 4 ways of another point in the same row, 3 ways of picking the third in the same row. Divide by 3*2*1 since the order in which these collinear points is picked does not matter. Multiply by two because the same argument applies for collinearity in columns. So answer = 2300 - 100 = 2200