Inspired by a recent Brainden puzzle, he layered his stack of fruit using triangular numbers. On top was a single orange. Beneath that was a layer of three oranges. In turn, the next layers had 6, 10, 15, 21, 28 and so on. until the oranges were used up. The entire stack, fortuitously, comprised a tetrahedron - a perfect triangular pyramid.
Until it was struck by the careless shopper making an illegal cell phone call while operating her shopping cart.
Faced with the task of reconstructing the citrus tower, the grocer opted for what he hoped was an easier task - to make two pyramids, unequal and smaller, but both still making perfect triangular structures.
Question
bonanova
A grocer had some oranges he wished to display.
Inspired by a recent Brainden puzzle, he layered his stack of fruit using triangular numbers. On top was a single orange. Beneath that was a layer of three oranges. In turn, the next layers had 6, 10, 15, 21, 28 and so on. until the oranges were used up. The entire stack, fortuitously, comprised a tetrahedron - a perfect triangular pyramid.
Until it was struck by the careless shopper making an illegal cell phone call while operating her shopping cart.
Faced with the task of reconstructing the citrus tower, the grocer opted for what he hoped was an easier task - to make two pyramids, unequal and smaller, but both still making perfect triangular structures.
How many oranges comprised the two pyramids?
Hint: there couldn't have been fewer.
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