Pascal's Pyramid

Probability Level 2

Imagine a pyramid made out of blocks, where the first layer has 1 block, the second layer is a 2×22\times 2 square made up of 4 blocks, the third layer is a 3×33\times 3 square made up of 9 blocks, and so on, so that each nthn^\text{th} layer is a square made from n2n^2 blocks.

Each block has a number written on it. The top block has the number 1 written on it, but every other block has the sum of all the blocks that touch its top side written on it. The first five layers are as follows:

What number would be written on the block that is in the 3rd3^\text{rd} column and 4th4^\text{th} row of the 100th100^\text{th} layer?

Note: This problem does not require a programming solution, although you may want to use a calculator for the last step!


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