> I'll have 5 times as many resistors if I put them on the cathodes, 
> reason being that I'll need to put them on the cathode for every
> column

Oh, yes, I see that now. Teach me to look to the right more often

But you could instead put 7 on the low side ? Each resistor is then
effective for a column, not a row. Compare yours with

http://www.mikroe.com/en/books/8051book/ch7/images/21.gif

Instead of R20 - 27, resistors could be on the collectors of Q1 - Q4

(You should adjust my column count in other posts from 6 to 7 BTW)

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