1 - Queen, 2 - Bishop, 3 - Knight, 4 - Rook
3 2 2 2 3 4 1 2
3 3 4 3 1 3 0 2
3 0 1 4 3 0 3 2
1 0 0 3 0 3 4 2
2 4 3 0 3 1 3 0
2 3 0 3 4 3 0 1
2 1 3 0 3 0 3 4
4 3 0 1 2 2 2 2
Xpress-Mosel Model
model 'crowd'
! Description : The crowded board
! Source : Dudeney, H.E., (1917), Amusements in Mathematics, Thomas Nelson and Sons.
! Date written : Xpress-MP May 2000, Mosel 19/4/03
! Written by : M J Chlond
uses 'mmxprs'
parameters
size = 8
piece = 4 ! 1 - Queen, 2 - Bishop, 3 - Knight, 4 - Rook
end-parameters
declarations
S = 1..size+4
P = 1..piece+4
R = 3..size+2 ! real part of board
N: array(P) of real
x: array(S,S,P) of mpvar
end-declarations
N:= [8,14,21,8]
any:= sum(i in R,j in R,k in P) x(i,j,k)
forall(k in P)
nump(k):= sum(i in R,j in R) x(i,j,k) = N(k)
forall(i in R,j in R)
onep(i,j):= sum(k in P) x(i,j,k) <= 1
! No queens attack each other
forall(i in R)
qrow(i):= sum(j in R) x(i,j,1) <= 1
forall(j in R)
qcol(j):= sum(i in R) x(i,j,1) <= 1
forall(i in 2..size+3)
qdia(i):= sum(k in 1..i) x(k,i-k+1,1) <= 1
forall(j in 1..size+3)
qdib(j):= sum(k in j..size+4) x(k,size+4-k+j,1) <= 1
forall(j in 1..size+3)
qdic(j):= sum(k in 1..size-j+5) x(k,j+k-1,1) <= 1
forall(i in 2..size+3)
qdid(i):= sum(k in i..size+4) x(k,k-i+1,1) <= 1
! No bishops attack each other
forall(i in 2..size+3)
bda(i):= sum(k in 1..i) x(k,i-k+1,2) <= 1
forall(j in 1..size+3)
bdb(j):= sum(k in j..size+4) x(k,size+4-k+j,2) <= 1
forall(j in 1..size+3)
dbc(j):= sum(k in 1..size-j+5) x(k,j+k-1,2) <= 1
forall(i in 2..size+3)
bdd(i):= sum(k in i..size+4) x(k,k-i+1,2) <= 1
! No rooks attack each other
forall(i in R)
rrow(i):= sum(j in 3..size+2) x(i,j,4) <= 1
forall(j in R)
rcol(j):= sum(i in 3..size+2) x(i,j,4) <= 1
! a(i,j,3) = 0 if square {i,i} attacked by knight
forall(i in R,j in R)
knta(i,j):= x(i-2,j-1,3) + x(i-1,j-2,3) + x(i+1,j-2,3) + x(i+2,j-1,3) +
x(i+2,j+1,3) + x(i+1,j+2,3) + x(i-1,j+2,3) + x(i-2,i+1,3) + 99*x(i,j,3) <= 99
! Dummy squares not occupied
setzero:= sum(i in 1..size+4,j in 1..size+4,k in 1..4 | i < 3 or i > size+2 or
j < 3 or j > size+2) x(i,j,k) = 0
forall(i in R,j in R, k in P)
x(i,j,k) is_binary
minimise(any)
forall(i in 1..size) do
forall(j in 1..size)
write(sum(k in P) k*getsol(x(i+2,j+2,k)),' ')
writeln
end-do
end-model