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For a display, identical cubic boxes are stacked in square layers. Eac [#permalink]
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Expert Reply
Basically we have a 9-layer pyramid as shown below:


Attachment:
pyramid_with_corner_cube_from_istock.jpg
pyramid_with_corner_cube_from_istock.jpg [ 9.54 KiB | Viewed 1169 times ]



(Actually this pyramid 8-layer, couldn't find 9-layer one image)

The number of boxes would be: \(9^2 + 8^2 + 7^2 + 6^2 + 5^2 + 4^2 + 3^2 + 2^2 + 1 = 285\).

You can use the sum of the first n perfect squares formula to calculate: \(\frac{n(n+1)(2n+1)}{6}=\frac{9*(9+1)(2*9+1)}{6}=285\).

Answer: E.
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Re: For a display, identical cubic boxes are stacked in square layers. Eac [#permalink]
Thank you
Carcass wrote:
Basically we have a 9-layer pyramid as shown below:


Attachment:
pyramid_with_corner_cube_from_istock.jpg



(Actually this pyramid 8-layer, couldn't find 9-layer one image)

The number of boxes would be: \(9^2 + 8^2 + 7^2 + 6^2 + 5^2 + 4^2 + 3^2 + 2^2 + 1 = 285\).

You can use the sum of the first n perfect squares formula to calculate: \(\frac{n(n+1)(2n+1)}{6}=\frac{9*(9+1)(2*9+1)}{6}=285\).

Answer: E.
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