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# 8 Queens or 1 to 50

Posts: 10,047

I had nothing better to do so I thought I’d write an 8 queens program. If you don’t know about it, you’re supposed to place 8 queens on an 8x8 board so that none of the queens can capture any other queen. There’s nothing fancy about the code or display. I was more curious as to how long or how many solutions there were per board. Once I had the 8 Queens going, I expanded it to do boards from sizes of 1 to 50. There are options to do single step, or change the speed from 1 step per draw cycle (default), up to 2,000,001 steps per draw cycle. You can select to print the solutions without stopping until it’s done or stop after each solution. You can play around with the selections to see how they work. This was more of just a hack job which I normally do with a lot of my code. When I can’t find anything better to do, I usually go back and rewrite the code to make it smaller and look better. But until then this will find the solutions, at least on the smaller boards, unless you want to wait awhile.

n=1 # of solutions = 1
n=2 # of solutions = 0
n=3 # of solutions = 0
n=4 # of solutions = 2
n=5 # of solutions = 10
n=6 # of solutions = 4
n=7 # of solutions = 40
n=8 # of solutions = 92
n=9 # of solutions = 352
n=10 # of solutions = 724
n=11 # of solutions = 2680
n=12 # of solutions = 14200

``````viewer.mode=STANDARD

function setup()
rectMode(CENTER)
parameter.integer("board",1,50,8,setup1)
parameter.integer("speed",0,20,0)
parameter.boolean("stop_on_solution",true)
parameter.boolean("single_step",false)
setup1()
end

function setup1()
output.clear()
check=false
count,count1=0,0
n=board
size=WIDTH/(n+3)
offset=1
queens={}
for z=1,n do
queens[z]=0
end
end

function draw()
background()
fontSize(size-5)
textMode(CENTER)
if check then
for t=1,100000*speed+1 do
if offset<1 then
return
end
if single_step then
speed=0
check=false
end
count1=count1+1
if checkRow() then
if checkDownDiag() then
if checkUpDiag() then
offset=offset+1
if offset>n then    -- solution
count=count+1
print(count.."="..table.concat(queens," "))
offset=offset-1
if stop_on_solution then
t=100000*speed+1
check=false
end
return
end
end
end
end
end
end
fill(255)
if stop_on_solution then
for x=1,n do
for y=1,n do
fill(255,0,0)
rect(x*size,y*size,size)
fill(255)
if queens[x]==y then
fill(0,0,255)
rect(x*size,y*size,size)
fill(255)
text(queens[x],x*size,y*size)
end
end
end
else
single_step=false
end

fontSize(20)
if not check then
text("Tap screen to continue",WIDTH/2,HEIGHT/2)
end
textMode(CORNER)
text("Draw Speed  "..speed*100000+1,10,HEIGHT-30)
text("Tries "..count1,WIDTH/2-60,HEIGHT-30)
text("Solutions "..count,WIDTH-150,HEIGHT-30)

end

function touched(t)
if t.state==BEGAN then
check=true
if offset<1 then
offset,count,count1=1,0,0
end
end
end

function addOne()   -- add 1 to column and zero columns to right
if offset<1 then
check=false
print("solutions complete")
return
end
queens[offset]=queens[offset]+1
if queens[offset]>n then
offset=offset-1
end
for z=offset+1,n do
queens[z]=0
end
end

function checkRow()
v=queens[offset]
for z=offset-1,1,-1 do
if v==queens[z] then
return false    -- another queen found
end
end
return true -- no other queens found
end

function checkDownDiag()    -- down and left
v=queens[offset]
b=1
if v==1 then    -- nothing to check
return true
end
for z=offset-1,1,-1 do
if v-b==queens[z] then
return false    -- another queen found
else
b=b+1
if v-b<1 then
return true
end
end
end
return true -- no other queens found
end

function checkUpDiag()  -- up and left
v=queens[offset]
b=1
if v==n then    -- nothing to check
return true
end
for z=offset-1,1,-1 do
if v+b==queens[z] then
return false    -- another queen found
else
b=b+1
if v+b>n then
return true
end
end
end
return true -- no other queens found
end
``````