So, while helping my mother clean out her closet (absolutely full of stuff she NEVER wears and stuff she's completely forgotten about), I found her father's old abacus. Green marble with brass beads and rods. When I eventually had to leave for an hour to let my sinuses rest from the dust in there, I learned how to work it....as far as addition and subtraction goes.

One thing, though, keeps hanging me up. whenever I add 123,456,789 to itself, I get the correct sum of 246,913,578. As part of an exercise I found online, I went further to add the original number to the sum again...but I can't get even halfway through figuring it out.

My step is this:
1- add 1 unit bead to the 2 to get three unit beads
2 - add 1 top-bead and subtract 1 unit bead to get 6 [ x+4=x-(5-1) ]
3 - I need to add three to the 6 is row 3...I COULD just add the three unit beads in that row...but that would throw off the end result.

According to the substitution rules used with an abacus, I could add one unit bead to the previous (left) row which represents an addition of 10, then simply subtract the number of beads in the current row to get what I need (subtracting 7 from the 10 added to equal an addition of 3). But I can't...not with 6.

I have no idea how to go about solving this fairly useless problem of mine.