Document 2.5: The Road Signs of Unspeakable Chaos

Your boss wrote:

I was consulted by the Minister of Transportation of the Realm of Unspeakable Chaos on a crisis they had. It turns out that a road sign was missing from their inventory and they needed a replacement. (This sign is an important clue.) Fortunately I was able to help him, since the road sign was available from another country. I've attached part of the inventory, which was hashed using the MD5 algorithm, then MIME base64 encoded, then lexicographically sorted.

Chaotians use the same language for road signs as they do for flags. (See earlier fieldwork notes from the Realm of Unspeakable Chaos at
http://web.mit.edu/puzzle/www/01/Solutions/chaotic.html.
The 2001 puzzle about flags and the Realm of Unspeakable Chaos is at:
http://wweb.mit.edu/puzzle/www/01/phase4/09/index.html for the puzzle or
http://web.mit.edu/puzzle/www/01/Solutions/realm.html for the solution.) Road signs are different from flags in a number of ways:

• Backgrounds are monochromatic.
• Road signs have no diminished shapes.
• The only colors used in road signs are black, yellow, white, and red.
• Road signs have no L-shapes or ^-shapes (inverted or not), nor do they have stars, dots, or horizontal lines.
• There are three other basic shapes:
• fruta = upward-pointing arrow
• pratu = rightward-pointing arrow
• babo = diamond
• There are three categories of shapes:
1. arrows, T-shapes, X-shape, Y-shapes
2. ring, triangles, diamond
3. /-shape, \-shape
• No more than two shapes of category 1 may appear on a sign.
• No more than one shape of category 2 may appear on a sign.
• No more than one shape of category 3 may appear on a sign.
• A sign must have a shape of category 1 or 2.
• Numbers are used exactly when describing category 1 shapes.
• If there are shapes of different categories on a sign, they are described in order of increasing category number, separated by 'pe'. Shapes of the same category should be separated by 'py', as they are for flags.
• All road signs are round.
• If there are two shapes of category 1, then they appear on the sign from left to right in the described order. No touching.
• Category 1 shapes are contained inside category 2 shapes if both are present. No touching.
• A category 3 shape is a diagonal line running from one side of the sign to another.
• In addition to inversives (see the field notes linked above), Chaotic has reflectives. The reflective of a noun (that is, a noun describing a shape just like the original, except flipped horizontally) is formed by making its first vowel a front vowel, and prepending a copy of this first vowel to the beginning of the word. If the inverse of a shape is the same as the reflection of the shape, then the inversive form of the noun is used.

All signs describable by the language should be present in a complete inventory (except of course those putting a shape on a background of the same color). Thereby explaining the name of the country!

(Example: a sign with a yellow background and two white leftward-pointing arrows in a black diamond is represented in the road sign language as "magare nasty enprety um pe dril babo" and is encoded as "XjDYbSl87wVZWBgZNGyTrg".)

The inventory extract: