Classic Problem: Census taker

count=0
for sum in range(1,36):
    for i in range(1,36):
        for j in range(1,36):
            for k in range(1,36):
                if(i*j*k==36 and i+j+k==sum):
                    count+=1
                    print(count,"sum ",i+j+k,i,j,k)

1 sum 10 3 3 4

2 sum 10 3 4 3

3 sum 10 4 3 3

4 sum 11 2 3 6

5 sum 11 2 6 3

6 sum 11 3 2 6

7 sum 11 3 6 2

8 sum 11 6 2 3

9 sum 11 6 3 2

10 sum 13 1 6 6

11 sum 13 2 2 9

12 sum 13 2 9 2

13 sum 13 6 1 6

14 sum 13 6 6 1

15 sum 13 9 2 2

16 sum 14 1 4 9

17 sum 14 1 9 4

18 sum 14 4 1 9

19 sum 14 4 9 1

20 sum 14 9 1 4

21 sum 14 9 4 1

22 sum 16 1 3 12

23 sum 16 1 12 3

24 sum 16 3 1 12

25 sum 16 3 12 1

26 sum 16 12 1 3

27 sum 16 12 3 1

28 sum 21 1 2 18

29 sum 21 1 18 2

30 sum 21 2 1 18

31 sum 21 2 18 1

32 sum 21 18 1 2

33 sum 21 18 2 1