Checkerboard squares?
There are many more different-sized squares on the chessboard. The complete list of answers is shown below: 1, 8x8 square 4, 7x7 squares 9, 6x6 squares 16, 5x5 squares 25, 4x4 squares 36, 3x3 squares 49, 2x2 squares 64, 1x1 squares There are 64 + 49 + 36 + 25 + 16 + 9 + 4 + 1 squares on a chessboard! (in total 204). http://www.teachingideas.co.uk/maths/chess.htm The formula which is the answer to Q1b is on the Math Forum below. Checkerboard Squares http://mathforum.org/library/drmath/view/56167.html
How many squares on a Checkerboard?
Well I know its 204 but, my teacher is an "think outside the box" kind of guy. So today he gave us a hint. The playing pieces are 65 but thats not it. So I did the math and got 204. But the 65 came from adding the whole board as 1 square plus the rest. So is the answer 205 or 204? Please help I cant do this even though I like math eqations and no website can answer this question. Thank you for all those genius's who help me!!!!
How many squares are in a 8x8 checkerboard?
1 8x8 4 7x7 9 6x6 16 5x5 25 4x4 36 3x3 49 2x2 64 1x1 sum(i=1 to 8; i^2) = 204 if you are allowing 1x1's
How many squares are in a 4x4 checkerboard?
HEY ! That's my homework too ! i got the answer . The problem is : : 1X1=1 2X2=4 3X3=9 4X4=16 You add all those together, and your answer is 30 ! ha ha loll !
Checkerboard squares?
Let's make n be the length of squares so an 8x8 is where n = 8. Start with n = 1 Obvious answer is 1 Go with n = 2 next You will have 4 little one and 1 2x2 one so 5 Move onto n = 3 next You will have 9 little ones 4 2x2 ones and 1 3x3 one so 14 Move onto n = 4 You will have 16 little ones 9 2x2 ones 4 3x3 ones and 1 4x4 so 30 Now let's look for patterns We have n = 1 and total 1 We have n = 2 and total 5 We have n = 3 and total 14 We have n = 4 and total 30 The pattern appears to be n^2 + (n-1). What this means is that you square the n value and add the previous value. So when n = 1 || 1 n = 2 || 2^2 + (1) = 5 n = 3 || 3^2 + (5) = 14 n = 4 || 4^2 + (14) = 30 n = 5 || 5^2 + (30) = 55 n = 6 || 6^2 + (55) = 91 n = 7 || 7^2 + (91) = 140 n = 8 || 8^2 + (140) = 204
How many squares on a 10x10 checkerboard? And is there some sort of formula?
385 squares ◄ Formula: Sum(11-n)^2, n=1 to 10. ◄ Here is how to derive the formula: Take a 3x3 square. How many places can it go? 8 rows by 8 columns. Right? which is 64 places which is (11-n)^2= (11-3)^2 And so on for the rest of the nxn squares.
How many squares are in a 3x3 checkerboard and 10x10?
This is basically just summing squares For a 3x3 checkerboard there are 1(1^2) 3x3 squares 4(2^2) 2x2 squares 9(3^2) 1x1 squares Summing together that makes 14 For the 10x10 you can just extend that pattern 1 10x10 4 9x9 9 8x8 16 7x7 25 6x6 36 5x5 49 4x4 64 3x3 81 2x2 100 1x1 When I summed them together i got 385 I also did the 8x8 and I got 204 as well I think the others don't understand your question In a 3x3 it is 14 in a 10x10 it is 385 From the pattern you should be able to see that the answer is n^2+(n-1)^2+(n-2)^2...1, which if you know summations can be written as the summation of x^2 from x=0 to x=n. (Summing all the squares from 1 to whatever "n" number) This is equal to n(2n+1)(n+1)/6 I knew the summation could be solved but I had to look up the exact equation and found the answer here http://answers.yahoo.com/question/index;_ylt=AoXOXFVfbjfuNqhORjpFEkYjzKIX;_ylv=3?qid=20080217211610AAOL7Zg