Checkerboard Square Pow
Essay by swim0017 • December 3, 2015 • Essay • 586 Words (3 Pages) • 1,795 Views
Problem Statement: An 8 by 8 checkerboard is made up of 64 smaller squares. You can combine the squares to form squares of other sizes. How many different squares can be found on a 8 by 8 checkerboard? What if the checkerboard was a different size. Say, 15 by 15. How would you determine the amount of squares on it?
Process: What I did first was I drew an 8 by 8 checkerboard of my own and started counting all of the possibilities.
I then realised that this process would take too long and that I had no patience for this. So I decided to re-read the question and think of another possible way to solve this problem. I thought about what we did in class on thursday and remembered PEMDAS. That was it! I realised that I could try multiplying instead of adding all of the squares. So I made a table counting all of the possible square sizes from 1 by 1 to 7 by 7.
8x8 size
12 =
1
7x7 size
22 =
4
6x6 size
32 =
9
5x5 size
42 =
16
4x4 size
52 =
25
3x3 size
62 =
36
2x2 size
72 =
49
1x1 size
82 =
64
Sum =
204
204
Finally!
This was my answer, 204.
Then I had to find a solution to the second problem. After reading it over carefully, I realised that I had to find an equation. So I asked for some help from my parents and we came up with this:
n(n+1)(2n+1)
Sum = ------------
6
After testing it out, the equation was correct.
Solution: I came up with 204 possible squares that can be found on an 8 by
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