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;
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So: sum = 1 + 2 + ... + side length = 1/2 * ( length + 1) * length;
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So the twelveth layer has 78 ;
So the grand total is:
1 + 3 + 6 + 10 + 15 + 21 + 28 + 36 + 45 + 55 + 66 + 78 = 364 !