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Checkerboard Square Pow

Autor:   •  October 4, 2017  •  593 Words (3 Pages)  •  539 Views

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8 checkerboard. I also came up with an equation, which is:

n(n+1)(2n+1)

Sum = ------------

6

If we use 8 by 8 as N, the equation is:

8(8+1)(2*8+1)

-

6

8*9=72

2*8=16+1=17

72*17=1224

1224/6= 204

It really helped to use a table because I could organise all of the gathered information, find a pattern (the exponents rose by one) and get an equation for the next question. I know that my answers are correct because when I solved question number one with my equation from question number two, I got 204. I don’t think that there is another answer because I found a pattern from my table, and following that pattern, there weren’t any other choices that I could make along the way.

Extensions: How many different squares can be found on a 20 by 20 checkerboard? How about an 8 by 8 checkerboard with one random square removed? Or a 6 by 7 checkerboard?

Self- assessment: Some of the things that I learned from this problem were that making a chart will almost always make solving a problem like this easier. I also learned that making an equation (if possible) will help you solve the problem quicker and will help you check if the problem is right. Another thing I learned is to read the problem carefully and not to rush but rather sit down and think about the problem. I think that I deserve an A because of all the time and effort I put into this assignment.

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