googling is usually the best way to find answers to math questions
like this.
regarding "how can be use?" - this is an excellent question. whether
the counters are "useful" is relative, but generally they are
demonstrations or exhibits. i "used" counters to make levels with the
most moves in a playback, "theoretical max", and the most shots in a
playback, "65,498 Shots, 2 Moves" (again - it may be debatable
whether this was actually a useful purpose :) i also tried to make
some hard counting levels (in Challenge-II.lvl) using counters almost
like a combination lock with many possible combinations, and people
figured them out by discovering how the counters worked, and not
trial and error. also, the really, really, really long levels show
how a lot of states, or information, might be packed into a small
space.
generally, these things are models of how things might work in the
real world inside various devices like computers, clocks, or
odometers. i also see that Alexis was successful in making a couple
of clock levels that keep track of hours minutes and seconds.
maybe now you can figure out a new "use" for counters.
good luck
-steve