Look at
http://www.misterinkjet.info/hp57reset.htm
I couldn't get this procedure to work with my 57 and 58 cartridges.
Although the basic idea is sound, I don't think you can say that all
cartridges will behave the same as they all have unique(ish) serial numbers
and taping can only change a 1 to a 0 or 0 to a 1, I don't know which but if
it's 0 to a 1 then if you tape over a contact that is set to 1 already then
nothing changes. Because of this I carried on experimenting till I found
contacts that did the trick and both my 57 and 58 cartridges reset correctly
by taping the blue one first as shown in the link above, and then the
contact below the blue one as well as the blue one. The red one wasn't
used. The third swap had no contacts taped over of course. It all takes a
while as you have to wait for a calibration page to be printed each swap.