yaworsw/euler-manager

---
:id: 309
:name: Integer Ladders
:url: https://projecteuler.net/problem=309
:content: "In the classic \"Crossing Ladders\" problem, we are given the lengths <var>x</var>
  and <var>y</var> of two ladders resting on the opposite walls of a narrow, level
  street. We are also given the height <var>h</var> above the street where the two
  ladders cross and we are asked to find the width of the street (<var>w</var>).\n\n
  ![p309_ladders.gif]({{ images_dir }}/p309_ladders.gif)\n\nHere, we are only concerned
  with instances where all four variables are positive integers.  \nFor example, if
  <var>x</var> = 70, <var>y</var> = 119 and <var>h</var> = 30, we can calculate that
  <var>w</var> = 56.\n\nIn fact, for integer values <var>x</var>, <var>y</var>, <var>h</var>
  and 0 \\< <var>x</var> \\< <var>y</var> \\< 200, there are only five triplets (<var>x</var>,<var>y</var>,<var>h</var>)
  producing integer solutions for <var>w</var>:  \n(70, 119, 30), (74, 182, 21), (87,
  105, 35), (100, 116, 35) and (119, 175, 40).\n\nFor integer values <var>x</var>,
  <var>y</var>, <var>h</var> and 0 \\< <var>x</var> \\< <var>y</var> \\< 1 000 000,
  how many triplets (<var>x</var>,<var>y</var>,<var>h</var>) produce integer solutions
  for <var>w</var>?\n\n"