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puzzle of the day

 
sona gold
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one side of the bottom layer of a triangular pyramid has 12 balls. How many are there in the whole pyramid?
 
John Lee
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Originally posted by sona nagee:
one side of the bottom layer of a triangular pyramid has 12 balls. How many are there in the whole pyramid?

I will try my best:
The top layer side length is 1 ball, layer sum is 1 ball;
The second layer side length is 2, layer sum is 3;
..................
So: sum = 1 + 2 + ... + side length = 1/2 * ( length + 1) * length;
................
So the twelveth layer has 78 ;
So the grand total is:
1 + 3 + 6 + 10 + 15 + 21 + 28 + 36 + 45 + 55 + 66 + 78 = 364 !
 
sona gold
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great Don.....
wait for a new one .. every day
 
Johnson Chong
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Hey! Don Liu, how come you have a 3D mind like that! Tell me pls, how long I got to wait for May and Susan?
 
John Lee
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Something tells me...
 
Johnson Chong
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Don Liu
Calculus of probabilities???!!!
What is that?
I've heard of calculus and probabilities but I just don't think I'll be able to find calculus of probabilities as a mathematical topic.
But I must say what a word.
 
Jim Yingst
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One of the definitions of calculus is "A system or method of calculation". So "calculus of probabilities" just means "calculation of probabilities". As it happens though, serious probability theory has lots of integrals in it, so you definitely need a good grasp of [integral] calculus to understand it.
 
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