5 is spelt "five". I don't understand how you decide what edges to draw in your nonogons. This is also known as addition mod 9. We can consider 9 the same as 0 (mod 9). We can sum two numbers and divide the sum by nine. The remainder is the answer. This is called addition mod 9.

Now the set 0, 1, ... , 8 is said to be a group under this operator because you trivially always get a value from that set when you add mod 9. The nonzero values do not form a group over multiplication mod 9. We have 3*3=0, which is out of the nonzero numbers. Zero can not be considered part of the group under multiplication mod 9 because there is nothing you can multiply by 0 that gives you 1.

In particular 1,4,7 is a group under multiplication mod 9. Now 2,5,8 and 3,6,9 are not. Now multiply by the elements of the group 2x(1,4,7) =(2,8,5) (mod 9) but 3x(1,4,7)=(3,3,3) and 6x(2,5,8) =(3,3,3) (mod 9).