yaworsw/euler-manager

---
:id: 202
:name: Laserbeam
:url: https://projecteuler.net/problem=202
:content: |+
  Three mirrors are arranged in the shape of an equilateral triangle, with their reflective surfaces pointing inwards. There is an infinitesimal gap at each vertex of the triangle through which a laser beam may pass.

  Label the vertices A, B and C. There are 2 ways in which a laser beam may enter vertex C, bounce off 11 surfaces, then exit through the same vertex: one way is shown below; the other is the reverse of that.

   ![]({{ images_dir }}/p201_laserbeam.gif)

  There are 80840 ways in which a laser beam may enter vertex C, bounce off 1000001 surfaces, then exit through the same vertex.

  In how many ways can a laser beam enter at vertex C, bounce off 12017639147 surfaces, then exit through the same vertex?