using JuMP
using MathProgBase
using GLPKMathProgInterface

# Create Mixed Integer Programming GLPK solver
m = Model(solver = GLPKSolverMIP())

# x[1] = S, x[2] = E, x[3] = N, x[4] = D, x[5] = M, x[6] = O, x[7] = R, x[8] = Y
@variable(m, 0 <= x[i=1:8] <= 9, Int)

# y[i,j] == 1 iff x[i] == j, 0 otherwise
@variable(m, y[i=1:8,j=0:9], Bin)

# Enforce sum consistency
@constraint(m, 1000*x[1] + 100x[2] + 10x[3] + 1x[4] + 1000x[5] + 100x[6] + 10x[7] + 1x[2] == 10000x[5] + 1000x[6] + 100x[7] + 10x[2] + 1x[8])

# Enforce that y[i,j] <=> x[i] == j
@constraint(m, [i=1:8], sum([j*y[i,j] for j=0:9]) == x[i])

# Enforce that each i has only one j associated to it (each letter has only one value)
@constraint(m, [i=1:8], sum([y[i,j] for j=0:9]) == 1)
# Enforce that eah j has at most one i associated to it (each digit appears in at most one letter)
@constraint(m, [j=0:9], sum([y[i,j] for i=1:8]) <= 1)

# Enforce that S >= 1 and M >= 1 because they are the leftmost digits of their respective words
@constraint(m, x[1] >= 1)
@constraint(m, x[5] >= 1)

print(m)

status = solve(m)

println("S = ", getvalue(x[1]))
println("E = ", getvalue(x[2]))
println("N = ", getvalue(x[3]))
println("D = ", getvalue(x[4]))

println("M = ", getvalue(x[5]))
println("O = ", getvalue(x[6]))
println("R = ", getvalue(x[7]))

println("Y = ", getvalue(x[8]))