yaworsw/euler-manager

---
:id: 412
:name: Gnomon numbering
:url: https://projecteuler.net/problem=412
:content: "For integers <var>m</var>, <var>n</var> (0&nbsp;≤&nbsp;<var>n</var>&nbsp;\\<&nbsp;<var>m</var>),
  let L(<var>m</var>,&nbsp;<var>n</var>) be an <var>m</var>×<var>m</var> grid with
  the top-right <var>n</var>×<var>n</var> grid removed.\n\nFor example, L(5, 3) looks
  like this:\n\n![p412_table53.png]({{ images_dir }}/p412_table53.png)\n\nWe want
  to number each cell of L(<var>m</var>,&nbsp;<var>n</var>) with consecutive integers
  1, 2, 3, ... such that the number in every cell is smaller than the number below
  it and to the left of it.\n\nFor example, here are two valid numberings of L(5,&nbsp;3):\n\n![p412_tablenums.png]({{
  images_dir }}/p412_tablenums.png)\n\nLet LC(<var>m</var>, <var>n</var>) be the number
  of valid numberings of L(<var>m</var>, <var>n</var>).  \nIt can be verified that
  LC(3,&nbsp;0) = 42, LC(5,&nbsp;3) = 250250, LC(6,&nbsp;3) = 406029023400 and LC(10,&nbsp;5)
  mod 76543217 = 61251715.\n\nFind LC(10000,&nbsp;5000) mod 76543217.\n\n"