yaworsw/euler-manager

---
:id: 359
:name: Hilbert's New Hotel
:url: https://projecteuler.net/problem=359
:content: "An infinite number of people (numbered 1, 2, 3, etc.) are lined up to get
  a room at Hilbert's newest infinite hotel. The hotel contains an infinite number
  of floors (numbered 1, 2, 3, etc.), and each floor contains an infinite number of
  rooms (numbered 1, 2, 3, etc.).\n\nInitially the hotel is empty. Hilbert declares
  a rule on how the <var>n</var><sup>th</sup> person is assigned a room: person <var>n</var>
  gets the first vacant room in the lowest numbered floor satisfying either of the
  following:\n\n- the floor is empty\n- the floor is not empty, and if the latest
  person taking a room in that floor is person <var>m</var>, then <var>m</var> + <var>n</var>
  is a perfect square\n\nPerson 1 gets room 1 in floor 1 since floor 1 is empty.  \nPerson
  2 does not get room 2 in floor 1 since 1 + 2 = 3 is not a perfect square.  \nPerson
  2 instead gets room 1 in floor 2 since floor 2 is empty.  \nPerson 3 gets room 2
  in floor 1 since 1 + 3 = 4 is a perfect square.\n\nEventually, every person in the
  line gets a room in the hotel.\n\nDefine P(<var>f</var>, <var>r</var>) to be <var>n</var>
  if person <var>n</var> occupies room <var>r</var> in floor <var>f</var>, and 0 if
  no person occupies the room. Here are a few examples:  \nP(1, 1) = 1  \nP(1, 2)
  = 3  \nP(2, 1) = 2  \nP(10, 20) = 440  \nP(25, 75) = 4863  \nP(99, 100) = 19454\n\nFind
  the sum of all P(<var>f</var>, <var>r</var>) for all positive <var>f</var> and <var>r</var>
  such that <var>f</var> × <var>r</var> = 71328803586048 and give the last 8 digits
  as your answer.\n\n"