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How many squares does an 8 by 8 checker board have? Please answer?
How many squares of all sizes (2 by 2, 3 by 3, 1 by 1, and so on) does an 8 by 8 checker board have?
If you answer correctly and timely I will give you all the points I can and answer any of your questions! Thank you so much(:
Beware of the overlapping squares!
There is 1 = 1² (8 by
square
There are 4 = 2² (7 by 7) squares
There are 9 = 3² (6 by 6) squares
There are 16 = 4² (5 by 5) squares [notice a pattern yet?]
There are 25 = 5² (4 by 4) squares
There are 36 = 6² (3 by 3) squares
There are 49 = 7² (2 by 2) squares
There are 64 = 8² (1 by 1) squares.
Thus, the total number of squares is
1² + 2² + 3² + ... + 8² = [8 · (8+1) · (2·8 +1)]/6 = 204.
--------------------------
In general, the total number of squares of an n by n checker board is
1² + 2² + 3² + ... + n² = n(n+1)(2n+1)/6.
I hope this helps!
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