From Newsgroup: rec.puzzles


I'm thinking of three sets (of bit-strings) which are conceptually infinite. Each of the sets is in practical use and has a name.
Here are the first twelve elements of each set:

(A)
1
000
010
00100
00110
01100
01110
0010100
0010110
0011100
0011110
0110100

(B)
11
011
0011
1011
00011
10011
01011
000011
100011
010011
001011
101011

(C)
00
01
100
101
1100
1101
11100
11101
111100
111101
1111100
1111101

Each of the infinite sets has the same special and useful property.
__ What is that property? __
Please rot13 any solution.

Dearest regards. James Dow Allen (mail address: jamesdowallen at gmail)
--- Synchronet 3.21b-Linux NewsLink 1.2

From Newsgroup: rec.puzzles



great problem!!!


James Dow Allen <user4353@newsgrouper.org.invalid> posted:

I'm thinking of three sets (of bit-strings) which are conceptually infinite. Each of the sets is in practical use and has a name.
Here are the first twelve elements of each set:

(A)
1
000
010
00100
00110
01100
01110
0010100
0010110
0011100
0011110
0110100

(B)
11
011
0011
1011
00011
10011
01011
000011
100011
010011
001011
101011

(C)
00
01
100
101
1100
1101
11100
11101
111100
111101
1111100
1111101

Each of the infinite sets has the same special and useful property.
__ What is that property? __
Please rot13 any solution.

Dearest regards. James Dow Allen (mail address: jamesdowallen at gmail)

--- Synchronet 3.21b-Linux NewsLink 1.2

From Newsgroup: rec.puzzles


James Dow Allen <user4353@newsgrouper.org.invalid> posted:

I'm thinking of three sets (of bit-strings) which are conceptually infinite. Each of the sets is in practical use and has a name.
Here are the first twelve elements of each set:

(A)
1
000
010
00100
00110
01100
01110
0010100
0010110
0011100
0011110
0110100

(B)
11
011
0011
1011
00011
10011
01011
000011
100011
010011
001011
101011

(C)
00
01
100
101
1100
1101
11100
11101
111100
111101
1111100
1111101

Each of the infinite sets has the same special and useful property.
__ What is that property? __
Please rot13 any solution.

As a hint, I'll provide another puzzle! This puzzle isn't really related
to the prior puzzle ("What special property do sets A, B and C have?"
although it implies a finite set with the same property) BUT it is a
puzzle in the SAME DOMAIN as the original puzzle.
Guess the relevant domain and both puzzles may fall into place.

As the hint/puzzle I define a transformation and then post a comment and
a challenge question about that transformation:

Transformation:
00 rRR 1
01 rRR 01
1 rRR 00

Comment: This .......... .... is essentially ....... over a binary ........ when the ........... .. . is a stationary 29%.

Question: What special property does this .......... .... have
which is quite rare among optimal .......... .....?


-----------------------
Dearest regards. James Dow Allen (mail address: jamesdowallen at gmail)
--- Synchronet 3.21b-Linux NewsLink 1.2

From Newsgroup: rec.puzzles


James Dow Allen <user4353@newsgrouper.org.invalid> posted:

James Dow Allen <user4353@newsgrouper.org.invalid> posted:

I'm thinking of three sets (of bit-strings) which are conceptually infinite.
...
Each of the infinite sets has the same special and useful property.
__ What is that property? __

As a hint, I'll provide another puzzle! ... a
puzzle in the SAME DOMAIN as the original puzzle.
Guess the relevant domain and both puzzles may fall into place.

Transformation:
00 rRR 1
01 rRR 01
1 rRR 00

Comment: This .......... .... is essentially ....... over a binary ........ when the ........... .. . is a stationary 29%.

Question: What special property does this .......... .... have
which is quite rare among optimal .......... .....?

Apparently my puzzles were either too difficult or too boring.
Please post a reply, however brief, if you even read the puzzles.

Cheers,
James
--- Synchronet 3.21b-Linux NewsLink 1.2

From Newsgroup: rec.puzzles

On Thu, 26 Feb 2026 10:41:28 GMT, James Dow Allen wrote:

Apparently my puzzles were either too difficult or too boring. Please
post a reply, however brief, if you even read the puzzles.

Hi James,

No, not boring - quite interesting.

Initially I was thinking of layers of bricks on a apex roof line - long
and short side on - Flemish-bond like. Not that, although I have been
thinking about a question related to the angle of an apex roof based on standard brick sizes and arrangements...

With the additional clue - I was thinking some sort of dither, or
something along the lines of NRZ coding, which I've come across in my
previous life. I don't think it's anything to do with that though. In some cases previous experience directs your thoughts and can be a hindrance to
more creative thought.

I think you've laid out what it is, but I can't see the exact algorithm,
or protocol to be applied. Somethings you see and something you don't. In
some ways, the things you don't see are more interesting than the things
you do, as you learn something new.

Best wishes,
--
David Entwistle
--- Synchronet 3.21b-Linux NewsLink 1.2

From Newsgroup: rec.puzzles

On Thu, 26 Feb 2026 10:41:28 GMT, James Dow Allen wrote:

Apparently my puzzles were either too difficult or too boring. Please
post a reply, however brief, if you even read the puzzles.

Cheers,
James

Am here, reading and enjoying the puzzling. Thank you and please keep 'em coming :)

- Matt
--- Synchronet 3.21b-Linux NewsLink 1.2

From Newsgroup: rec.puzzles


James Dow Allen <user4353@newsgrouper.org.invalid> posted:

James Dow Allen <user4353@newsgrouper.org.invalid> posted:

I'm thinking of three sets (of bit-strings) which are conceptually infinite.
Each of the sets is in practical use and has a name.

I don't want to just blurt out the answer. So I'll show some nice
properties that the sets have:

Here are the first twelve elements of each set:

The elements of (A) have lengths 1,3,3,5,5,5,5,7,7,7,7,7,... respectively.
If the bits are 50-50 coin tosses, then from a given starting point
'000' will occur with probability 1/8; and so on.

(A)
1 --> 1 ... 1/2
000 --> 3 ... 1/8
010 --> 3 ... 1/8 (or 1/2^3)
00100 \
00110 \
01100 / --> 5,5,5,5 ... 4/32 (or 4/2^5)
01110 /
0010100 \
0010110 \
0011100 / --> 7,7,7,7,7 ... 5/128 (or 5/2^7)
0011110 /
0110100 /

1/2 + 1/8 + 1/8 + 4/32 + 5/128 = 0.914
But these are INFINITE sets. If we continue, get
1/2 + 1/8 + 1/8 + 4/32 + 8/128 + 16/512 + 32/2048 + 64/8192 +... = 0.992 Asymptotic to 1. This is a necessary but insufficient condition for sets
with all the special properties.

Repeat this for set (B) and get
1/4 + 1/8 + 2/16 + 3/32 + 5/64 + 8/128 + 13/256 + 21/512 + 34/1024
+ 55/2048 + 89/4096 + 144/8192 + 233/16384 + 377/32768 = 0.951 ...
Also converging to 1, but very slowly.
By the way, dig those numerators?! There are 1, 1, 2, 3, 5, 8 tokens
of length 2, 3, 4, 5, 6, 7, respectively.

Another nifty feature of set (B) is that it is a place-value representation (with an extra 1 appended) of the natural numbers:

(B)

... 12358

11 = 1 (always ignore the terminal 1; it is used as a "comma.")
011 = 2
0011 = 3
1011 = 1+3
00011 = 5
10011 = 1+5
01011 = 2+5
000011 = 8
100011 = 1+8
010011 = 2+8
001011 = 3+8
101011 = 1+3+8

... 12358

Every element of set (B) terminates with '11' but never has other
instances of '11' inside.

A typical computer program would spend 8 bits (00000011) to represent
the very small integer 3. And would be unable to represent any
integer larger than 255 (11111111).
But (B) uses only 4 bits (0011) to represent 3. And there is no limit
to the size of integers which can be represented.
In what application domain would this be useful?

(C) is also a simple rendering of the natural numbers
(though now 0 is included).

(C)
00 = 0
01 = 1
100 = 2+0
101 = 2+1
1100 = 2+2+0
1101 = 2+2+1
11100 = 2+2+2+0
11101 = 2+2+2+1
111100 = 2+2+2+2+0
111101 = 2+2+2+2+1
1111100 = 2+2+2+2+2+0
1111101 = 2+2+2+2+2+1

Each of the infinite sets has the same special and useful property.
__ What is that property? __

The way that '11' serves as a terminator in (B) above may offer a hint
to the solution of this puzzle.

Cheers,
James
--- Synchronet 3.21b-Linux NewsLink 1.2

From Newsgroup: rec.puzzles

On 26/02/2026 10:41, James Dow Allen wrote:

James Dow Allen <user4353@newsgrouper.org.invalid> posted:

James Dow Allen <user4353@newsgrouper.org.invalid> posted:

I'm thinking of three sets (of bit-strings) which are conceptually infinite.
...
Each of the infinite sets has the same special and useful property.
__ What is that property? __

As a hint, I'll provide another puzzle! ... a
puzzle in the SAME DOMAIN as the original puzzle.
Guess the relevant domain and both puzzles may fall into place.

Transformation:
00 rRR 1
01 rRR 01
1 rRR 00

Comment: This .......... .... is essentially ....... over a binary ........ >> when the ........... .. . is a stationary 29%.

Question: What special property does this .......... .... have
which is quite rare among optimal .......... .....?

Apparently my puzzles were either too difficult or too boring.
Please post a reply, however brief, if you even read the puzzles.

Cheers,
James

Not boring at all, but... I don't always see an answer, especially a full answer, and time is
limited!...

So looking at your original post, I see some properties, but don't really have a full answer!

The sequences remind me of Huffman codes, and Huffman codes wouldn't work if sequences of them
couldn't be uniquely interpreted. Your sets have this property, so we could say they're like an
infinite set of Huffman codes(?).

Worded differently, all your sets seem to have the property that no two strings start with the same
prefix. We could interpret them as finite nodes in an infinite binary tree, and each of these nodes
has the property that its path does not pass through any other nodes.

Also, it seems the sets of nodes are constructed (more or less) by some kind of fractal pattern.
E.g. set A seems to have a generator pattern (apart from the entry 1):

A
/ \
/ \
x x
/ \ / \
N A N A

where we paste the root A where it occurs below. The Ns are the terminal nodes, which are the ones
in your set A, which appears to be listed in order depth then left-to-right. (Left being
represented as 0, Right as 1).

I'd guess the sets might be related to compression of infinite stream data??? Perhaps used somehow
in video codecs? but I don't see exactly how, or know what their names would be.

Other observations: For all the sets there are infinite paths that have no prefix in the set. Set
A has uncountably many of these, e.g. 0010101010101... or 0111101011101... (basically, as long as
odd-numbered digits (other than the first) are 1). All the sets have "enough" nodes so that a
random path hits a node "almost certainly" (i.e. with probability 1). I don't know if that is
important.

But no end of other sets have these same properties - even if the "fractal" property is key. (I
suppose that might be important when processing an infinite stream, because only a finite amount of
context data would have to be maintained.


Regards,
Mike.

--- Synchronet 3.21b-Linux NewsLink 1.2

From Newsgroup: rec.puzzles


(In my most recent post I suggested by example that the "Krafft sum"
was asymptotically one, where each token in the set contributes 2^(-k)
to the Krafft sum where k is the number of bits in that token.)


Mike Terry <news.dead.person.stones@darjeeling.plus.com> posted:

On 26/02/2026 10:41, James Dow Allen wrote:

James Dow Allen <user4353@newsgrouper.org.invalid> posted:

James Dow Allen <user4353@newsgrouper.org.invalid> posted:

I'm thinking of three sets (of bit-strings) which are conceptually infinite.
...
Each of the infinite sets has the same special and useful property.
__ What is that property? __

Not boring at all, but... I don't always see an answer, especially a full answer, and time is
limited!...

So looking at your original post, I see some properties, but don't really have a full answer!

The sequences remind me of Huffman codes, and Huffman codes wouldn't work if sequences of them
couldn't be uniquely interpreted. Your sets have this property, so we could say they're like an
infinite set of Huffman codes(?).

Kudos to Mike Terry! These are exactly like Huffman codes; a more general
term is compaction codes. In a finite world, no token will actually be infinite but it is convenient to define mappings of the integers which are unbounded.

A "Huffman code" is a compaction code which is optimal for some particular probability mass function. But EVERY compaction code with Krafft sum of one will be optimal for SOME distribution.

Worded differently, all your sets seem to have the property that no two strings start with the same
prefix.

Yes. These are called "prefix codes" or "prefix-free codes" or
(old-fashioned term?) "instantaneous codes." Not all compaction codes
are instantaneous, cf arithmetic or quasi-arithmetic codes.

We could interpret them as finite nodes in an infinite binary tree, and each of these nodes
has the property that its path does not pass through any other nodes.

Also, it seems the sets of nodes are constructed (more or less) by some kind of fractal pattern.
E.g. set A seems to have a generator pattern (apart from the entry 1):

A
/ \
/ \
x x
/ \ / \
N A N A

where we paste the root A where it occurs below. The Ns are the terminal nodes, which are the ones
in your set A, which appears to be listed in order depth then left-to-right. (Left being
represented as 0, Right as 1).

I'd guess the sets might be related to compression of infinite stream data??? Perhaps used somehow
in video codecs? but I don't see exactly how, or know what their names would be.

Other observations: For all the sets there are infinite paths that have no prefix in the set. Set
A has uncountably many of these, e.g. 0010101010101... or 0111101011101... (basically, as long as
odd-numbered digits (other than the first) are 1). All the sets have "enough" nodes so that a
random path hits a node "almost certainly" (i.e. with probability 1). I don't know if that is
important.

Wow, and Kudos again. I think this is all correct.

But no end of other sets have these same properties - even if the "fractal" property is key. (I
suppose that might be important when processing an infinite stream, because only a finite amount of
context data would have to be maintained.

Yes. Kudos AGAIN to Mike!

For example, consider (B) where a token terminates if and only if a '11'
is encountered. There is a code with tokens terminating if and only if
a '111' is encountered. Or even a code which terminates at '1101010' !

I worked with these things back in the 20th century, so talking about them is
a trip down Nostalgia Lane for me. PLEASE help me present puzzles better. Should I have provided more hints to start? Wait longer for responses?


The codes (A), (B), (C) have names. (B) is the "Fibonacci Code."
(C) is the "Golomb (or Golomb-Rice) Code with divisor 2."

I don't know the "official" name of (A) -- in fact I'd be unaware of it
except that its co-inventor and I both consulted for the same company
in the mid-1990s. I will call (A) "a version of the Elias Gamma Code with
a palindromic property." Look again at (A); erase the 2nd, 4th, 6th bits,
etc. The bit-strings left are all palindromes. (And Mike suggested this.)
If a data stream is corrupted one can find a synchronization point and then decode BACKWARDS to the point of corruption, perhaps recovering all but one token.


FINALLY:

As a hint, I'll provide another puzzle! ... a
puzzle in the SAME DOMAIN as the original puzzle.
Guess the relevant domain and both puzzles may fall into place.

Transformation:
00 rRR 1
01 rRR 01
1 rRR 00

The coded-token set {1, 01, 00} is a simple prefix code, satisfying the Krafft Equality
1/2 + 1/4 + 1/4 = 1.

(BTW, for this and similar codes if the input data ends with an odd number
of 0's an extra 0 is injected at the end and later removed during decompaction.)
(The LENGTH of input data is generally knowable.)

Comment: This compaction code is essentially optimal over a binary alphabet when the probability of '1' is a stationary 29%.

STILL UNSPOILED:

Question: What special property does this compaction code have
which is quite rare among optimal compaction codes?

Cheers,
James
--- Synchronet 3.21b-Linux NewsLink 1.2

From Newsgroup: rec.puzzles

On 27/02/2026 06:25, James Dow Allen wrote:

(In my most recent post I suggested by example that the "Krafft sum"
was asymptotically one, where each token in the set contributes 2^(-k)
to the Krafft sum where k is the number of bits in that token.)

Mike Terry <news.dead.person.stones@darjeeling.plus.com> posted:

On 26/02/2026 10:41, James Dow Allen wrote:

James Dow Allen <user4353@newsgrouper.org.invalid> posted:

James Dow Allen <user4353@newsgrouper.org.invalid> posted:

I'm thinking of three sets (of bit-strings) which are conceptually infinite.
...
Each of the infinite sets has the same special and useful property.
__ What is that property? __

Not boring at all, but... I don't always see an answer, especially a full answer, and time is
limited!...

So looking at your original post, I see some properties, but don't really have a full answer!

The sequences remind me of Huffman codes, and Huffman codes wouldn't work if sequences of them
couldn't be uniquely interpreted. Your sets have this property, so we could say they're like an
infinite set of Huffman codes(?).

Kudos to Mike Terry! These are exactly like Huffman codes; a more general term is compaction codes. In a finite world, no token will actually be infinite but it is convenient to define mappings of the integers which are unbounded.

A "Huffman code" is a compaction code which is optimal for some particular probability mass function. But EVERY compaction code with Krafft sum of one will be optimal for SOME distribution.

Worded differently, all your sets seem to have the property that no two strings start with the same
prefix.

Yes. These are called "prefix codes" or "prefix-free codes" or (old-fashioned term?) "instantaneous codes." Not all compaction codes
are instantaneous, cf arithmetic or quasi-arithmetic codes.

We could interpret them as finite nodes in an infinite binary tree, and each of these nodes
has the property that its path does not pass through any other nodes.

Also, it seems the sets of nodes are constructed (more or less) by some kind of fractal pattern.
E.g. set A seems to have a generator pattern (apart from the entry 1):

A
/ \
/ \
x x
/ \ / \
N A N A

where we paste the root A where it occurs below. The Ns are the terminal nodes, which are the ones
in your set A, which appears to be listed in order depth then left-to-right. (Left being
represented as 0, Right as 1).

I'd guess the sets might be related to compression of infinite stream data??? Perhaps used somehow
in video codecs? but I don't see exactly how, or know what their names would be.

Other observations: For all the sets there are infinite paths that have no prefix in the set. Set
A has uncountably many of these, e.g. 0010101010101... or 0111101011101... (basically, as long as
odd-numbered digits (other than the first) are 1). All the sets have "enough" nodes so that a
random path hits a node "almost certainly" (i.e. with probability 1). I don't know if that is
important.

Wow, and Kudos again. I think this is all correct.

But no end of other sets have these same properties - even if the "fractal" property is key. (I
suppose that might be important when processing an infinite stream, because only a finite amount of
context data would have to be maintained.

Yes. Kudos AGAIN to Mike!

Hey, I'm running out of room for storing all my Kudoses! :)

For example, consider (B) where a token terminates if and only if a '11'
is encountered. There is a code with tokens terminating if and only if
a '111' is encountered. Or even a code which terminates at '1101010' !

I worked with these things back in the 20th century, so talking about them is a trip down Nostalgia Lane for me. PLEASE help me present puzzles better. Should I have provided more hints to start? Wait longer for responses?

I remember covering Huffman codes back in my student days (studying maths), but more recently I was
looking at some C code to implement LZ-compression which uses Huffmamn codes, so I was kind of
primed to recognise this feature. One of my (mild) regrets was that my work (corporate IT stuff)
didn't really utilise my maths abilities, but hey, I did ok out of it, so no complaints. (I'm
retired now.)

I think you are fine with your puzzle presentations so I don't have any recomendations for you.
This particular puzzle probably suffered a bit from being unclear what its objective was. There was
no spider which had to catch a fly! :) The topic in itself has some interest (for me) but is maybe
too technical for lots of people. Also, I think the old days of rec.puzzles are long gone, and
there are now not many "puzzle people" left... (HenHanna may keep the newsgroup ticking over, but
very few of his posts are actually "puzzles" in the traditional sense - mostly they're questions
about language use...)

Mike.

The codes (A), (B), (C) have names. (B) is the "Fibonacci Code."
(C) is the "Golomb (or Golomb-Rice) Code with divisor 2."

I don't know the "official" name of (A) -- in fact I'd be unaware of it except that its co-inventor and I both consulted for the same company
in the mid-1990s. I will call (A) "a version of the Elias Gamma Code with
a palindromic property." Look again at (A); erase the 2nd, 4th, 6th bits, etc. The bit-strings left are all palindromes. (And Mike suggested this.) If a data stream is corrupted one can find a synchronization point and then decode BACKWARDS to the point of corruption, perhaps recovering all but one token.

FINALLY:

As a hint, I'll provide another puzzle! ... a
puzzle in the SAME DOMAIN as the original puzzle.
Guess the relevant domain and both puzzles may fall into place.

Transformation:
00 rRR 1
01 rRR 01
1 rRR 00

The coded-token set {1, 01, 00} is a simple prefix code, satisfying the Krafft Equality
1/2 + 1/4 + 1/4 = 1.

(BTW, for this and similar codes if the input data ends with an odd number
of 0's an extra 0 is injected at the end and later removed during decompaction.)
(The LENGTH of input data is generally knowable.)

Comment: This compaction code is essentially optimal over a binary alphabet when the probability of '1' is a stationary 29%.

STILL UNSPOILED:

Question: What special property does this compaction code have
which is quite rare among optimal compaction codes?

Cheers,
James

--- Synchronet 3.21b-Linux NewsLink 1.2

From Newsgroup: rec.puzzles

On Fri, 27 Feb 2026 06:25:04 GMT, James Dow Allen wrote:

I worked with these things back in the 20th century, so talking about
them is a trip down Nostalgia Lane for me. PLEASE help me present
puzzles better. Should I have provided more hints to start? Wait longer
for responses?

Hi James,

That is interesting. Thanks for the question and explanation. I'm
following it to some extent.

Would it be practical to provide a real-World, or 'puzzle-World', scenario where the sequences, with the given properties, provide a solution to a problem the inhabitants faced? Crash survivors, on two islands,
communicating with limited means - that sort of thing... I find that understanding a problem gives weight to the solution.

I like pictures and there is a nice one (possibly related) here:

https://en.wikipedia.org/wiki/Zeckendorf%27s_theorem

Best wishes,
--
David Entwistle
--- Synchronet 3.21d-Linux NewsLink 1.2

From Newsgroup: rec.puzzles


David Entwistle <qnivq.ragjvfgyr@ogvagrearg.pbz> posted:

Would it be practical to provide a real-World, or 'puzzle-World', scenario where the sequences, with the given properties, provide a solution to a problem the inhabitants faced? Crash survivors, on two islands, communicating with limited means - that sort of thing... I find that understanding a problem gives weight to the solution.

Maybe, but I probably lack the imagination to come up with such an idea. Communication with aliens? A property of optimal compaction is that the compressed form appears random, so indecipherable.

There are some documents from the early 1600s which allegedly contain
cryptic messages. A task for those with good intuition is to guess
whether such messages are genuine, or arise by chance. Would 1 or 2
of such alleged encryptions be of interest? But the aliens could begin
by listing the coded integers, much as I did in (B) of the first post
in this thread.

I like pictures and there is a nice one (possibly related) here:

https://en.wikipedia.org/wiki/Zeckendorf%27s_theorem

Yes, that article and its references show why (B) above ("the Fibonacci code") works. I notice cites to a paper which makes the observation I made, that strings other than '11' can be used as the delimiting comma, also achieving instantaneous decoding with the Krafft equality implying optimality.

I recognized the name of the author -- Jarek Duda. You can see at
https://arxiv.org/pdf/1206.4555
that I helped him with a combinatorial problem many years ago.
Specifically I showed him how to replace a bound of (QQQ + 2.71828)
with (QQQ + 0.57721)*, a rather amazing change since Euler's number
gets changed to the seemingly-unrelated Euler's constant.
* - The actual improvement was similar to, but less than, this
(2.71828 - 0.57721) but I cannot remember details.

Cheers,
James
--- Synchronet 3.21d-Linux NewsLink 1.2

From Newsgroup: rec.puzzles


Just a reminder that one puzzle has not yet been explicitly solved.
The "puzzle" isn't difficult, but stating the solution should elicit
at least a tiny "WOW!"

STILL UNSPOILED:

Question: What special property does the compaction code [shown below] have
which is quite rare among optimal compaction codes?

James Dow Allen <user4353@newsgrouper.org.invalid> posted:

Mike Terry <news.dead.person.stones@darjeeling.plus.com> posted:

On 26/02/2026 10:41, James Dow Allen wrote:

James Dow Allen <user4353@newsgrouper.org.invalid> posted:

James Dow Allen <user4353@newsgrouper.org.invalid> posted:

FINALLY:

As a hint, I'll provide another puzzle! ... a
puzzle in the SAME DOMAIN as the original puzzle.
Guess the relevant domain and both puzzles may fall into place.

Transformation:
00 rRR 1
01 rRR 01
1 rRR 00

Comment: This compaction code is essentially optimal over a binary alphabet when the probability of '1' is a stationary 29%.

STILL UNSPOILED:

Question: What special property does this compaction code have
which is quite rare among optimal compaction codes?

Cheers,
James

--- Synchronet 3.21d-Linux NewsLink 1.2

From Newsgroup: rec.puzzles

On Sat, 28 Feb 2026 06:13:22 GMT, James Dow Allen wrote:

Just a reminder that one puzzle has not yet been explicitly solved. The "puzzle" isn't difficult, but stating the solution should elicit at
least a tiny "WOW!"

I think I'm slightly lost, but did find the following web page somewhat illuminating:

https://james.fabpedigree.com/appixm.htm

In general, in this puzzle, we could be talking about reducing the size of source code for very constrained computer architectures; is that correct?

I did like the last paragraph comment, from the web page, "decoded in
either direction". That is neat. You may have already mention that here.

Best wishes,
--
David Entwistle
--- Synchronet 3.21d-Linux NewsLink 1.2

From Newsgroup: rec.puzzles

On Sun, 1 Mar 2026 10:55:33 -0000 (UTC), David Entwistle wrote:

In general, in this puzzle, we could be talking about reducing the size
of source code for very constrained computer architectures; is that
correct?

Apologies, I think I meant to say reducing the size of machine code, not source code. So, variable-length binary information. It's been a long time since I looked at anything like that. I suspect my experience-bias to a
bus architecture is is proving a barrier to seeing the environment.
--
David Entwistle
--- Synchronet 3.21d-Linux NewsLink 1.2