Question 753607: A sports store owner is a making a display with 200 baseballs. He is placing them in the shape of a square pyramid. The bottom layer has 64 baseballs placed in the shape of a square. For each consecutive layer of baseballs, one baseball is placed where 4 baseballs meet. How many layers will be in the pyramid? How many baseballs will be left over?
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! For each pair of rows on the bottom layer, there are 7 positions where 4 balls meet, and there are 7 such pairs of rows on the bottom layer.
Similarly, for the 3rd row there are 6 positions for each pair of rows and 6 pairs of rows.
And so on, up the pyramid.
So the number of balls in successive rows are squares of integers counting down from 8:
8^2,7^2,6^2,...
64+49+36+25+16+9 = 199
So there is one ball left over
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