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Geek Culture / How many blocks in a pyramid?

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Libervurto
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Joined: 30th Jun 2006
Location: On Toast
Posted: 21st Aug 2010 19:11
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This seems like a pretty simple maths problem but I can't find an answer!
I want a formula that will return the number of blocks in a pyramid given the number in the base.

I only want this for a 2D pyramid where n is the height of the pyramid and also the number of blocks in the base.

I know you can say

but there must be a proper formula for working this out.

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IanM
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Location: In my moon base
Posted: 21st Aug 2010 21:51
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It's fairly easy:

Row 1: 1 block
Row 2: 2 blocks
Row 3: 3 blocks
Row 4: 4 blocks
Row 5: 5 blocks

It's easy to see the progression from that. If you draw it out in a certain way, then you can work out the formula fairly easily:

#xxxxx
##xxxx
###xxx
####xx
#####x

=> (5 * (5 + 1)) / 2
=> (5 * 6) / 2
=> 30 / 2
=> 15 ... which happens to be the right answer.

In general, the formula would by (n * (n + 1)) / 2 which works for any number of rows.

Utility plug-ins collection (updated 26 July 2010) and
http://www.matrix1.demon.co.uk
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Libervurto
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Posted: 22nd Aug 2010 06:58 Edited at: 22nd Aug 2010 07:08
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Ah, thanks Ian.

so a 3D one would be

x = blocks
1 = 1
2 = 5 = 4+1
3 = 14 = 9+5
4 = 30 = 16+14
n = ? = n^2+?

blocks = n^2*(n+1)/2 ?

no i need to think about this

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Green Gandalf
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Playing: Malevolence:Sword of Ahkranox, Skyrim, Civ6.
Posted: 22nd Aug 2010 12:33
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Quote: "no i need to think about this"


Just do what Ian did for 2D:
1
4
9
16
.
.
.
n^2

so you want the sum of the first n squares. It's a standard result from school maths:

(n * (n + 1) * (2n + 1)) / 6

Use Google.
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Libervurto
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Posted: 23rd Aug 2010 05:38
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Thanks, my maths sucks.
I did use google it had nothing useful.

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Green Gandalf
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Posted: 23rd Aug 2010 21:13
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Quote: "I did use google it had nothing useful."


I guess you asked the wrong question. Through sheer laziness I got the answer from Google immediately. I searched for formula for the sum of squares and one result even gave the formula in the Google summary.
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