A cruel and fickle king

Algebra Level 4

For the past decade, the king of Mathlandia has forced his subjects to build a pyramid in his honor. The king decreed the pyramid to be constructed with cubic stone slabs. The king decreed the pyramid to be built in 100 square levels, with each subsequent level 2 units less on a side than the previous level. The top level was to be constructed with a single cube. (See the picture for an example of a pyramid 3 levels high constructed in the same way).

Moments after the final cube was placed, the king changed his mind. He ordered the pyramid to be taken down, and in its place, a cubic monolith was to be built. He ordered the monolith to be built as large as possible with the same stone slabs the pyramid was made of.

The king decided that he would tolerate no waste, and so he ordered one of his subjects to be sacrificed for each leftover slab of stone.

How many of the king's subjects will be sacrificed?


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