Geography Quiz

James Allen:

Brazil??

Without checking, I think that maybe...

25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2

they form the vertices of a cube, or as close to a cube as you can get with all the vertices on land. I recall seeing a puzzle posted here some years ago that asked for the construction of exactly that figure...

1. Cocos Islands ('Keeling Islands' 2. Christchurch, New Zealand 3. Honolulu, Hawaii 4. Bodaybo, Russia 5. Punta Peclas, Nicaragua ('Mosquito Coast' 6. Vigo, Spain 7. Ghanzi, Botswana 8. Cape Horn, Brazil

Except for Ghanzi, near the Kalahari Desert, all the above places are near a major body of water, indeed near a major land/water feature. (Bodaybo is 300 km. NE of Lake Baikal's tip; Vigo is near the corner of Spain where Bay of Biscay begins.)

But something much more remarkable links these 8 places. What is it?

Sorry about the Cape Horn, 'Brazil'...

Cube it is...

Google used to post in '6 to 9 hours' but now posts 'immediately.' Mark Brader (is he on vacation in Tahiti or working graveyard shift in Toronto) are almost in a 'chat room'

How about any of the other regular solids?

Cheers!

Mark Brader mentioned that such cubes had been mentioned in rec.puzzles recently; I found a mention with a Google search: http://groups-beta.google.com/group/rec.puzzles/msg/ c5b75360a6cb1a54 (BTW, Google no longer provides friendly support for viewing Usenet messages; anyone know of an alternative for Internet cafe users?)

That thread suggests more puzzles:

Puzzle 1: Find eight points on the Earth's *land* surface that form a perfect cube. (I use the approximation that the Earth is a perfect sphere.)

Comment: My solution with Cocos Island comes *much* closer than any other near-solution I've found, but my database of obscure mid-ocean islands is far from complete. I don't think even my solution works perfectly: the antipodes of Cocos Islands may all be some miles to sea off the coast of Nicaragua.

Puzzle 2: The old thread asks: Find eight points on the surface of a sphere maximizing the minimum distance among point pairs.

Comment: As pointed out in the old thread, a cube is *not* optimal.

Puzzle 3: Same as Puzzle 2, but replace 'eight' with 4, 5, 6, 7, 9, etc.

Comment: This must be an anciently studied puzzle. Given my Alzheimer's symptoms, I may well have read about it here 15 years ago and forgotten.

Puzzle 4: If my calculation is correct, the best puzzle-3 solution for 5 yields a minimal distance no larger than the 6-solution so call 5 a 'useless' number. Find all useless numbers.

Comment: There should be only a finite number of them, right? James Dow Allen

See Part 1, Dimension 3 of <http://www.research.att.com/~njas/packings/index.html> .

Looking at the above reference, I'd guess that the only other useless number is 11.

rot13(fdhner nagvcevfz). David Cantrell's web page confirms this.