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The Cannon-balls riddle

A ship sailor has stacked cannon-balls in two tetrahedral pyramids. In order to impress the ship captain he decided to combine the cannon-balls in both of the pyramids and create one large pyramid. The smallest number of cannon-balls he can have if the two pyramids are the same size is twenty ( we assume that he uses every cannon-ball in both pyramids).You can see that solution in the picture below.

  tetrahedral pyramids piles to visualize the math problem

  However if the two smaller pyramids are different sizes what would be the minimum number of cannon-balls he could use to make one larger tetrahedral pyramid?

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