yaworsw/euler-manager

---
:id: 154
:name: Exploring Pascal's pyramid
:url: https://projecteuler.net/problem=154
:content: |+
  A triangular pyramid is constructed using spherical balls so that each ball rests on exactly three balls of the next lower level.

   ![]({{ images_dir }}/p154_pyramid.gif)

  Then, we calculate the number of paths leading from the apex to each position:

  A path starts at the apex and progresses downwards to any of the three spheres directly below the current position.

  Consequently, the number of paths to reach a certain position is the sum of the numbers immediately above it (depending on the position, there are up to three numbers above it).

  The result is _Pascal's pyramid_ and the numbers at each level <var>n</var> are the coefficients of the trinomial expansion (<var>x + y + z</var>)<sup><var>n</var></sup>.

  How many coefficients in the expansion of (<var>x + y + z</var>)<sup>200000</sup> are multiples of 10<sup>12</sup>?