Multiple-Aspirin Headache

From a book (whose title I cannot mention, 'cuz it would
be a clue) by Thomas L. Saaty and Paul C. Kainen.
Okay okay this is yer basic generic geopolitical MAP.

Maybe it's a map of the counties in your state or nation. Maybe it's a map of some of the states of the USA; or the provinces of Canada. Maybe it's the nations of Eurasia, or Africa, or South America. You get the idea. Each region shares borders with neighboring regions.

Now suppose you want to publish this map with different colors so that

        No Two Regions with a Common Border
                Have the Same Color.

In other words, Scotland has to be a different color from England; Jordan has to be a different color from Israel; Texas has to be a different color from Oklahoma.

What's the FEWEST NUMBER of different colors you need to do this?

Grab this image and draw different numbers (1,2,3 ...) inside each region to indicate a distinct color. (Don't just e-mail me back "EIGHT!" I need to see HOW you did it.)

When you've colored it with the Fewest Colors Possible, send it back to me and if you solve it,
Miss Florence Diner chow, your name here to show you are smarter than Pakleds, etc.
 

Okay! Promptness is Good!allicatof Undernet/#tmbg= Megan of Oz gave this a whack, sent it back, and I pronounce her solution Correct! Close on her heels comes another correctly-colored map from John Moriarty = BillNyefrom the Bizarro #tmbg on EfNet.

The rest of you: Keep trying!

What we got here  is a mildly tough example map associated with the famous
N-Color Problem (I still ain't disclosing what N is) that made aspirin companies wealthy
from 1852, when Francis Guthrie first posed it (using the counties of England as the example),
to 1976, when it was finally proved and forever laid to rest.

Now actual map-printers had long ago worked up their own minimum N number of different ink colors from experience. Geopolitical maps and borders are always changing, but they'd never encountered a map which demanded more than this number of colors, so they just never stocked more inks than that.

But the trick is to prove somehow that N-minimum can color any imaginable, possible, conceivable map (on a plane or on the surface of a sphere). Or, if you're certain it's N, the trick for someone else is to cook up just one weird-looking map which inescapably requires N+1 colors.

Yeah, it certainly looks like a Math(s) Thang -- but notice how arithmetic and geometry don't seem to be much use to solve it, or algebra, or trig, or calculus. So maybe it's more a Logic Thang.

If you think this coloring-book exercise is a walk in the park, consider Herman Minkowski, who supplied much of the math Einstein needed to make Relativity get off the runway. Minkowski told his class one day that the reason N-Color had never been proved was because only second-rate mathematicians had worked on it. "I believe I can prove it," he declared. A very long time later, he announced:
                                "Heaven is angered by my arrogance.
                                 My proof is also defective."

When I get enough solutions, I'll let you know who finally proved it, what N-minimum for all possible maps turned out to be, and tell you the very unique and controversial story about this proof.



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The Rules of Go

1. Go is played on a 19 x 19 grid of intersecting rectangular lines, by two players:
   black, who has a bowl of black stones, and white, with a bowl of white stones.
    At the start of the game, the board is empty.

2. Black goes first by placing a stone on any intersection, called a point.
    (Points at the board's edges are legal.) Thereafter, white and black alternate.
    A player may pass (place no stone) at any time.

3. Once a stone is placed on the board, it stays there for the rest of the game,
    unless captured.

4. If one or more stones of Player A are completely surrounded by stones of
    Player B, the A stones are captured and removed. (Captured stones are placed
    in the bowl lid of the capturer.)

    If Player B can completely surround one or more of Player A's stones,
    this situation is called atari. Player A doesn't have to defend his/her
    threatened stone(s).

                   Left: Three white stones in atari.
                 Center: Black moves, surrounding white stones.
                  Right: White stones are removed.

    When Player A's stones are in atari, Player A can't kill his/her own stones.
      Only Player B can kill and capture A's stones.

5. It's illegal to make a move which recreates a previous board pattern.

6. If a player passes twice in a row, the game ends. Or a player may resign.

7. At the end of the game, all stones which can't avoid capture are removed.

8. A player's score is the number of vacant points it has surrounded, minus the
    number of its captured stones. High score wins.

There's a handicap system, agreed informally between players, or decided by the official ratings of experienced players. (Handicap rating is called dan or kyu.) At the start of the game, the weaker player takes black, and places from one to nine stones on points marked by special dots. Then white makes its first move.

Beginners often play on boards smaller than 19 x 19; or book examples of rules and strategic situations use smaller boards. 9 x 9 is the common beginners' board. For obvious reasons, a lot of computer Go experimenting uses smaller boards.

Adapted from An Introduction to Go,
by James Davies and Richard Bozulich, 1990, Ishi Press.

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a Personal Testament
 

Given the existence as uttered forth in the public works of Puncher and Wattmann of a personal God quaquaquaqua with white beard quaquaquaqua outside time without extention who from the heights of divine apathia divine athambia divine aphasia loves us dearly with some exceptions for reasons unknown but time will tell and suffers like the divine Miranda with those who for reasons unknown but time will tell are plunged in torment plunged in fire whose fire flames if that continues and who can doubt it will fire the firmament that is to say blast hell to heaven so blue still and calm so calm with a calm which even though intermittent is better than nothing but not so fast and considering what is more that as a result of the labors left unfinished crowned by the Acacacacademy of Anthropopopometry of Essy-in-Possy of Testew and Cunard it is established beyond all doubt all other doubt than that which clings to the labors of men that as a result of the labors unfinished of Testew and Cunard it is established as hereinafter but not so fast for reasons unknown that as a result of the public works of Puncher and Wattmann it is established beyond all doubt that in view of the labors of Fartov and Belcher left unfinished for reasons unknown of Testew and Cunard left unfinished it is established what many deny that man in Possy of Testew and Cunard that man in Essy that man in short that man in brief in spite of the strides of alimentation and defecation wastes and pines wastes and pines and concurrently simultaneously what is more for reasons unknown in spite of the strides of physical culture the practice of sports such as tennis football running cycling gliding comating camogie skating tennis of all kinds dying flying sports of all sorts autumn summer winter winter tennis of all kinds hockey of all sorts penicilline and succedanea in a word I resume flying gliding golf over nine and eighteen holes tennis of all sorts in a word for reasons unknown in Feckham Peckham Fulham Clapham namely concurrently simultaneously what is more for reasons unknown but time will tell fades away I resume Fulham Clapham in a word the dead loss per head since the death of Bishop Berkeley being to the tune of one inch four ounce per head approximately by and large more or less to the nearest decimal good measure round figures stark naked in the stockinged feet in Connemara in a word for reasons unknown no matter what matter the facts are there and considering what is more much more grave that in the light of the labors lost of Steinweg and Peterman it appears what is more much more grave that in the light the light the light of the labors lost of Steinweg and Peterman that in the plains in the mountains by the seas by the rivers running water running fire the air is the same and then the earth abode of stones in the great cold the great dark the air and the earth abode of stones in the great cold alas alas in the year of their Lord six hundred and something the air the earth the sea the earth abode of stones in the great deeps the great cold on sea on land and in the air I resume for reasons unknown in spite of the tennis the facts are there but time will tell I resume alas alas on on in short in fine on on abode of stones who can doubt it I resume but not so fast I resume the skull fading fading fading and concurrently simultaneously what is more for reasons unknown in spite of the tennis on on the beard the flames the tears the stones so blue so calm alas alas on on the skull the skull the skull the skull in Connemara in spite of the tennis the labors abandoned left unfinished graver still abode of stones in a word I resume alas alas abandoned unfinished the skull the skull in Connemara in spite of the tennis the skull alas the stones Cunard tennis ... the stones ... so calm ... Cunard ... unfinished ...

It just doesn't happen to be my Personal Testament. Whose is it? Please feel free to share your feelings about these thoughts. Most important, are there any mistakes or typos here? Was I perfect? This thing was a five-alarm nightmare to type.

Remember the people who memorize books in Bradbury's Fahrenheit 451? I'd like to join the hundreds of people, maybe thousands by now, who've memorized this. Yes, hundreds, maybe thousands of people have memorized every word of this perfectly. No jive. I kid you not. Are we talking cult here? You decide.

Usual deal, e-mail, your name here proclaiming that you're smarter than Pakleds, food at Miss Flo's, etc.

Okay! John Moriarty a.k.a. BillNye (from the
Bizarro #tmbg on EfNet, where a robot curses you for using colors and slapping it with a trout) says he had to sweat and actually research this one, but he got it! He is smarter than Pakleds, and the honeycomb tripe at the MFD awaits him.

Now I'm getting a little tired of always seeing the same hands ...

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