/* 

  Wee equation in Picat.

  From Chris Smith's Math Newletter #549
  """
  Please find me the value of the positive integers 
  a,b,d,d that satisfy this wee equation

     a +  1            = 266/115
         ----
         b + 1
            ------
            c + 1/d
  """

  (Wee (Scottish): little)

  There's a single solution: [2,3,5,7]
  

  Mathematica give this unique solution:
  In[1]:= FindInstance[{a + (1/(b + 1/(c + 1/d))) == 266/115, a > 0, 
           b > 0, c > 0, d > 0}, {a, b, c, d} \[Element] Integers, 10]
  Out[1]= {{a -> 2, b -> 3, c -> 5, d -> 7}}

  This model was created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Picat page: http://www.hakank.org/picat/

*/

import cp.

main => go.

go ?=>
  L = [A,B,C,D],
  L :: 1..100,
  
  % A + 1 / (B + 1 / ( C + 1/D)) #= 266/115,
  % 
  % However, using "/" is not a good thing so we rewrite
  % to just additions and multiplications.
  % 
  % Mathematica:
  % In[2]:= Factor[A + 1 / (B + 1 / ( C + 1/D)) == 266/115]                                                     
  % 
  %         1 + A B + A D + C D + A B C D    266
  % Out[2]= ----------------------------- == ---
  %                 B + D + B C D            115
  % 
  T1 #= 1 + A*B + A*D + C*D + A*B*C*D,
  T2 #= B + D + B*C*D,
  % T1 / T2 #= 266/115,
  T1*115 #= T2*266,

  solve($[degree,updown],L),
  println(L),
  fail,
  
  nl.
go => true.