/* 

  100 left-hand people problem in Picat.

  From MindYourDecisions
  https://www.youtube.com/watch?v=gLN_0K6JnPs
  """
  The British Game Show The 1% Club featured this very interesting riddle for an 
  accumulating jackpot of £97,000.

  “In a room of 100 people, 99% are left-handed. How many left-handed people have to 
  leave the room to bring that percentage down to 98% ?”
  """

  Perhaps it should have stated _exactly_ 98%?

  pct_before = 0.99
  [leaving = 50,num_left = 50,numLeftHandledLeft = 49]
  pct_after = 0.98
      
  This program was created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Picat page: http://www.hakank.org/picat/

*/

% import util.
import cp.

main => go.

go ?=>
  N = 100, % Number of people in the room
  L = 99,  % Number of left handed people in the room
  _R = 1,   % Number of right handed people in the room

  println(pct_before=(L/N)),

  Leaving :: 1..99, % Number of left handed people leaving the room
  NumLeft #= N-Leaving, % Number of people left in the room
  NumLeftHandedLeft #= L-Leaving, % Number of left handle left handed people left
  98*NumLeft #= 100*NumLeftHandedLeft, % 98 #= 100*L2/N2, but CP does not like divisions
  Vars = [Leaving,NumLeft,NumLeftHandedLeft],
  solve(Vars),
  println([leaving=Leaving,num_left=NumLeft,numLeftHandledLeft=NumLeftHandedLeft]),
  println(pct_after=(NumLeftHandedLeft/NumLeft)),
  fail,
  
  nl.
go => true.