> For example whenever I try to power digit 6, the digit '1' will glow
> as well in one tube. If I connect digit '1' directly, '6' will also
> partially light up.
> 
> Any idea how to fix this?

I had this problem with my GR-1620* when I got it.  A close look revealed that 
one arm of the "Kg" cathode
had gotten hooked on the "t" cathode.  I suppose this happened during shipping 
when it got knocked in a
particular direction.  So I considered the supports, lengths, weights, and 
arrangement of things and decided
that a reasonable rap in a particular direction would likely pop them free of 
each other.  I folded a towel and
placed it on a table, gripped the tube firmly, and, greatly daring, tapped it 
in the way I had worked out.  I didn't
fix it, and I could feel/hear the elements vibrating.  So I tried a little 
harder and it worked!  The tube works perfectly
now.

* http://www.vitriol.com/images/tech/nixies/nixies-huge.jpeg

With your tube, it's worth a try, as the tube has limited usefulness if you can 
not light the 1 or 6 separately.  With
smaller tubes (as I assume yours is, compared to a GR-1620), everything is 
lighter and stiffer, so it would take more
impact to cause and (hopefully) fix such entanglement.  But it's worth a try, 
if you can't otherwise use the tube.

> I also have an NL tube of which the digit 6 never glows, instead the
> wire connecting the pin & digit gives light.

That's probably a broken connection.  Fixing that without opening the tube 
doesn't seem likely (maybe, if there were a laser that could go through glass 
but be absorbed by metal, you could spot-weld the wire from outside, but that's 
just not likely).

> I'm wondering if I am
> really digit 6 killer...

With two tubes, the chance is 1 in 5* (since two digits are involved in one 
tube), so given a single instance, it's not remarkable.  If you randomly 
acquired a third tube, and it also had issues with 6, you're down to 1/25.  A 
fourth tube,
and you're past the 1% level, and I'd start to wonder about it.  At first, I 
thought it was a variant of the Birthday Problem,
but then I realized this would be the case where *all* the tubes shared the 
same digit, which is a different kettle of fish.

* Actually slightly different, due to the way digits are stacked in tubes, 
where adjacent digits are much more likely to
short than non-adjacent digits, which skews the probabilities in subtle and 
complicated ways.

Birthday Problem:

http://www.npr.org/templates/story/story.php?storyId=4542341

- John

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