Solution

            1  0  1  1  0
            0  1  1  1  0
            1  1  1  0  0
            1  1  0  1  1
            0  0  0  1  1


Xpress-Mosel Model
model 'five'

! Description  : 5 X 5 puzzle
! Source       : Unknown
! Date written : MAGIC 10/11/92, Xpress-MP 5/4/98, Mosel 17/4/03
! Written by   : M J Chlond

  uses 'mmxprs'

  parameters
    n = 5
  end-parameters 

  declarations
    N = 1..n
    x: array(N,N) of mpvar 
    d: array(N,N) of mpvar
  end-declarations

  moves:= sum(i in N, j in N) x(i,j)

  forall(i in N,j in N)
    con(i,j):= sum(k in j-1..j+1 | k >= 1 and k <= n and k <> j) x(i,k)+
               sum(k in i-1..i+1 | k >= 1 and k <= n) x(k,j) = 2*d(i,j)+1 

  forall(i in N,j in N) do
    x(i,j) is_binary
    d(i,j) is_integer
  end-do

  minimise(moves)

  forall(i in N) do
    forall(j in N)
      write(getsol(x(i,j)),' ')
    writeln
  end-do

end-model