Country count
Michael, if it helps, I've attached a list of the 192 "core countries" that
seem to have the most wide-spread recognition. Any tripoint survey would also
have to take into account at least the existence of French Guiana, an
Overseas Department of France with a debated/approximate borders with
Suriname and Brazil. This, I think, is the only land-surface boundary between
country and dependency. If you are going to use nautical boundaries (as it
seems to me you are), then there may be other dependency-related borders out
there.

Exclaves
I thought I had detected a subtle variant use of the word "exclave" by this
group, which I liked. But maybe I'm wrong, in which case my recent
enclave/exclave dichotomies are meaningless. I certainly agree with a
previous mail from Brendan that the perfectly complimentary dictionary
definitions of ex/enclaves is confusing and pointless - basically two names
for the same thing: a bit of one country enclosed by another. But although I
can't find it in a handy dictionary today, is there not another, more general
usage, of "exclave", to mean any detached part of a parent country (Brendan's
"fragment")? In terms of etymology, such a usage is at least defensible:
enclave = something enclosed within a country; exclave = something detached
from a country. With such usage the exclave/enclave contrast becomes useful,
and allows us to sort the territory into four basic categories from which we
can build.

Indian/Bangla enclaves
I had assumed that the oft-quoted 111 and 51 enclaves represented the *total*
count - ie including enclaves-within-enclaves. But, Brendan, your recent
posting seems to suggest that the 2nd and 3rd order enclaves need to be
*added* to this total. That is:
111 Indian enclaves + 3 Indian 2nd order enclaves + 1 Indian 3rd order enclave
51 Bangladeshi enclaves + 21 Bangladeshi 2nd order enclaves.
Is that correct?
(I'm accepting here that the exact figures are unknown, as you've already
said.)

Why enclaves happen
Finally, addressing the notion of enclaves as signs of the spread and
recession of nations, I've always had a different picture in my head, which I
might as well throw into the pot. Borders are simple lines traced in two
dimensions (on the surface of a map, a globe or the wrinkled real world), but
people distribute themselves *fractally* - little outlying patches of folk,
with their own little outliers, with *their* own outliers, right down to the
three Lithuanian guys on the lupin farm in Belarus. So *any* attempt to draw
a 2-D line of demarcation across a populated landscape is flawed to some
extent, because fractals are (2+a fraction)-dimensional. Possible solutions
are:
a) Draw the border through uninhabited territory (desert or frontier
countries)
b) Use huge natural divides (rivers, mountains) to minimise the fractal
overspill
c) Move the people (the Partition solution)
d) Ignore their wishes (the chopping up of Africa, in many places)
e) Enclaves

Grant