Asked by Carly
You decide to build a pyramid out of wooden blocks. Each block must rest on the corners off 4 other blocks. If there is one block on top and 36 on the bottom, what is the total number of blocks you will need to complete the pyramid?
Answers
Answered by
Reiny
The top layer has 1 block
the 2nd layer from the top has 4 blocks
the 3rd layer from the top has 9 blocks
the 4th has 16 blocks
the 5th has 25 blocks, and
the 6th has s36 blocks
So we have 1+4+9+16+25+36
= 91
btw, there is a formula for the sum of squares of the first n numbers
sumofsquares(n) = n(n+1)2n+1)/6
sumofsquares(6) = 6(7)(13)/6 = 91
the 2nd layer from the top has 4 blocks
the 3rd layer from the top has 9 blocks
the 4th has 16 blocks
the 5th has 25 blocks, and
the 6th has s36 blocks
So we have 1+4+9+16+25+36
= 91
btw, there is a formula for the sum of squares of the first n numbers
sumofsquares(n) = n(n+1)2n+1)/6
sumofsquares(6) = 6(7)(13)/6 = 91
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