LPL - A Mathematical Modeling Language

model hikers "Who Went Hiking Alone?";
  set i,j:=[A B C D E F G H I J K L M N O P Q];
    e{i,j} := 
      [(A,*) F G H O , (B,*) A C G H , (C,*) D J K M
       (D,*) C E P Q , (E,*) D F K O , (F,*) A E G H
       (G,*) C E F J , (H,*) E F I K , (I,*) A G K L
       (J,*) G I L P , (K,*) G H L Q , (L,*) J M N O
       (M,*) A C L N , (N,*) D L O P , (O,*) E L N Q
       (P,*) D J M N , (Q,*) D K N O];
  set k:=[1..4];
  binary variable x{i,k};
  constraint A{i}: sum{k} x = 1;
  constraint B{k,e[i,j]}: x[i,k] + x[j,k] <= 1;
  constraint C: sum{i} x[i,4]=1;
  constraint D: sum{i} x[i,3]=3;
  --constraint E: x['I',4]=0;
  solve;
    
  parameter 
    X{i}:=[8 2 0 8 16 14 5 11 8 4 12 8 7 8 9 6.3 9.7];
    Y{i}:=[11 11 7 0 7 11 9 9 7 6 6 5 4 2 4 2 2];
  Draw.Scale(50,50);
  {e[i,j]} Draw.Line(X[i],Y[i],X[j],Y[j]);
  --{i,k|x} Draw.Circle(i&'',X,Y,.3,1,0);
  {i,k|x} Draw.Circle(i&'',X,Y,.3,k+2,0); 
end

Original version:
A group of 17 prisoners - A to Q - have to work in three different hospitals. 
One day, a grocery store in the neigborhood is robbed. The store owner is absolutely 
sure that the thief was one of the prisoners. Unfortunately, there is no fixed 
working schedule, so every prisoner can decide on how own where he wants to work 
on a certain day. The three hospitals give us the following information: three 
prisoners worked in the first hospital, six of them worked in the second hospital 
and seven worked in the last hospital. Adding these numbers shows that one of the 
prisoners did not work on that day. Since the prisoners don't want to incriminate 
one of there cell mates, they don't want to tell where and who they worked with on
the concerning date. After a long discussion they agree to a compromise: every 
prisoner names four persons who he didn't work with. This leads to the following 
Table.

\begin{table}[htbp]
  \centering
  \caption{Conclusion of the prisoners statements}
    \begin{tabular}{rrrrrrrr}
    Prisoner & mentions &       & Prisoner & mentions &       & Prisoner & mentions \\
    A     & F, G, H O &       & G     & C, E, F, J &       & M     & A, C, L, N \\
    B     & A, C, G, H &       & H     & E, F, I, K &       & N     & D, L, O, P \\
    C     & D, J, K, M &       & I     & A, G, K, L &       & O     & E, L, N, Q \\
    D     & C, E, P, Q &       & J     & G, I, L, P &       & P     & D, J, M, N \\
    E     & D, F, K, O &       & K     & G, H, L, Q &       & Q     & D, K, N, O \\
    F     & A, E, G, H &       & L     & J, M, N, O &       &       &  \\
    \end{tabular}%
  \label{tab:addlabel}%
\end{table}%
Assuming that every prisoner said the truth, is it possible to find the thief?
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Mathematical Modeling with LPL : Explain and run a Model