reset;

option solver cplex;                            # solver choice
#option solver './minos';                       # fuer macOS

param n := 4;									# square size
param N := n^2;									# numbers
param C := n*(n^2+1)/2;	   						# target sum

var x {i in 1..n,j in 1..n,k in 1..N} binary;	# binary variables

subject to NB1{j in 1..n}: sum{i in 1..n,k in 1..N} k*x[i,j,k] = C;  
subject to NB2{i in 1..n}: sum{j in 1..n,k in 1..N} k*x[i,j,k] = C;  
subject to NB3{i in 1..n,j in 1..n}: sum{k in 1..N}   x[i,j,k] = 1;  
subject to NB4{k in 1..N}: sum{i in 1..n,j in 1..n}   x[i,j,k] = 1;  

solve;	   										# solution

var y {i in 1..n,j in 1..n}=sum{k in 1..N} k*x[i,j,k];	# transformed

display y;	   									# output