! Lottery ticket covering problem. Which combination of tickets should
   we buy so we win, regardless of the outcome. Cast in the form of 
   betting on the outcome of a number of futbol games.
 Ref: Linderoth, J., F. Margot, ang G. Thain(2009),
   "Improving Bounds on the Football Pool Problem by
    Integer Programming and High-Throughput Computing",
     INFORMS Journal of Computing, vol. 21, no. 3, pp. 445-457;
SETS:
 OUTK1;
 OUTK2;
 OUTK3;
 OUTK4;
 OUTK5;
 OUTK6;
 COMBO( OUTK1,OUTK2,OUTK3,OUTK4,OUTK5,OUTK6): Y;

ENDSETS
DATA:
  OUTK1 = WIN LOSE DRAW;
  OUTK2 = WIN LOSE DRAW;
  OUTK3 = WIN LOSE DRAW;
  OUTK4 = WIN LOSE DRAW;
  OUTK5 = WIN LOSE DRAW;
  OUTK6 = WIN ;!LOSE DRAW;
ENDDATA
  
! Known results:
      # Games   Tickets must buy
         1          1
         2          3
         3          5
         4          9
         5         27
         6       71<= t <= 73
;
  ! Y(i1, i2, i3, i4, i5, i6) = 1 if we buy a ticket that bets
   on outcome (i1, i2, i3, i4, i5, i6);
  MIN = @SUM( COMBO(i1, i2, i3, i4, i5, i6): Y(i1, i2, i3, i4, i5, i6));

  ! Make them binary;
   ! @FOR( COMBO(i1, i2, i3, i4, i5, i6): @BIN(Y(i1, i2, i3, i4, i5, i6)));


  ! For each game and each outcome, at least one of our choices
  must be close enough. We are close enough if we got only one wrong;
  @FOR( COMBO( i1, i2, i3, i4, i5, i6): 
    Y( i1, i2, i3, i4, i5, i6) ! Get all right;
      ! or get exactly 1 outcome wrong ;
   +@SUM( COMBO(k1, i2, i3, i4, i5, i6) | k1 #NE# i1 : Y(k1, i2, i3, i4, i5, i6))
   +@SUM( COMBO(i1, k2, i3, i4, i5, i6) | k2 #NE# i2 : Y(i1, k2, i3, i4, i5, i6))
   +@SUM( COMBO(i1, i2, k3, i4, i5, i6) | k3 #NE# i3 : Y(i1, i2, k3, i4, i5, i6))
   +@SUM( COMBO(i1, i2, i3, k4, i5, i6) | k4 #NE# i4 : Y(i1, i2, i3, k4, i5, i6))
   +@SUM( COMBO(i1, i2, i3, i4, k5, i6) | k5 #NE# i5 : Y(i1, i2, i3, i4, k5, i6))
        >= 1;
      );

  ! Kill some symmetry;
     Y(1, 1, 1, 1, 1, 1) = 1;