Wine Cask Puzzle II

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Problem

This problem is related to math09.


Listing 1: The Complete Model implemented in LPL [2]
model math09a "Wine Cask Puzzle II"; 
  set n,m:=[nephew1 nephew2 nephew3 nephew4 nephew5]; 
      c:=['Empty' '1/4'  '1/2'  '3/4'  'Full']; 
  parameter  HOWFULL{c} := [0 0.25 0.5 0.75 1]; 
  integer variable x{n,c} [1..5]; 
  constraint 
    A{n}: sum{c} x = 9; 
    B{c}: sum{n} x = 9; 
    C{n}: sum{c} HOWFULL*x = 4.5; 
    F{n,m|n>m}: or{c} (x[n,c]<>x[m,c]); 
  solve; 
  Writep(x); 
end

References

[1]   MatMod. Homepage for Learning Mathematical Modeling :  https://matmod.ch.

[2]   Hürlimann T. Reference Manual for the LPL Modeling Language, most recent version. https://matmod.ch/lpl/doc/manual.pdf.