Wolfe's Puzzles

Thomas Bitterman · 10 Jul 2010, 12:52 · from 2010-July.txt.gz

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From: tom at bitterman.net (Thomas Bitterman)
Date: Sat, 10 Jul 2010 08:52:29 -0400
Subject: (urth) Wolfe's Puzzles
In-Reply-To: <SNT123-W52AE66C3C8EA2DAECC1441CFB60 at phx.gbl>
References: <SNT123-W52AE66C3C8EA2DAECC1441CFB60 at phx.gbl>
Message-ID: <AANLkTikmIeIeU_n7kVzB3skJ-rD0I3UFH1W4MaMhjMS4 at mail.gmail.com>

On Sat, Jul 10, 2010 at 1:51 AM, Lee Berman <severiansola at hotmail.com>wrote:

>
> Anyway, the group came to one puzzle that none of us could make heads nor
> tails of, including Mantis, (at least I inferred that from his silence). It
> regarded a series of numbers, arranged in a pattern which was found on the
> Seal of Pas.
>
> 5553  8783  4223  9700  34
>
> 2221  0401  1101  7276  56
>
> SEALED FOR THE MONARCH
>

Some facts:
They are not SSCC-18 barcodes - the check digit is incorrect.
They are not credit card numbers - they fail the Luhn test.
The sum of the digits of all the 4 digit numbers and the sum of the digits
of all the 2 digit numbers is the same: 9.

Odd observations:
All 4-digit numbers have two digits that are the same.  That seems unlikely.
None of the digits in the two-digit numbers are doubled in the same row.
Each 4-digit number is larger than the one below it.
Subtracting the bottom 4-digit number from its corresponding top yields
another set of 4-digit numbers, all of which have doubled digits.

My guess is that the 4-digit groups are the "product" code, and the 2-digit
groups are checksums.  This is similar to how lots of different encoding
schemes work and makes sense in this context.  It only gives one-bit error
detection, so there may be another layer of checking I've missed.  Maybe
something having to do with the doubled digits.

As far as the product code itself goes, that might take a little more work.
Wolfe was an engineer and did some robotics work, so maybe Gray or Huffman
coding is being used.

I am no cryptographer type but I gamely gave the puzzle a few days of
> intense thought and effort. I mostly tried combinations of adding the
> numbers together, since Silk makes the sign of addition over them
> (and various other things) I tried working in base 9 since that
> might be in use in Viron math. No luck. I could not come up with an answer.
>

It shouldn't be base 9.  There is a 9 in the code, and base n doesn't use a
symbol for n.
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