| Title: | Mathematics at DEC |
| Moderator: | RUSURE::EDP |
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
Here is a varient of an old and familiar game: The game is played on an n x n rhombus of points connected in a hexagon pattern (so each interior point is connected to 6 neighbors). Players Red and Black alternate in placing markers of their respective colors on some unoccupied intersection on the board. A player wins if there is a path passing only through intersections with his markers on them which joins one side of the rhombus to the other. (Note that either player can witn either "vertically" or "horizontally" - the edges don't come pre-colored. Show that there is always a winner. -- Jerry Hint: Generalize.
| T.R | Title | User | Personal Name | Date | Lines |
|---|---|---|---|---|---|
| 517.1 | a start | SIERRA::OSMAN | and silos to fill before I feep, and silos to fill before I feep | Tue Jun 17 1986 16:47 | 36 |
I call the game HEX. It's one of my favorites, after GO of
course.
To clarify this rhombus business, the HEX board is a honeycomb
pattern, with equal rows and columns.
If any of you have a VAXSTATION 100, try my HEX program !
(Hey Jerry, I notice there's a VAXSTATION 100 here in the QA
lab)
To show that there is always a winner, I'd suggest trying to
generate an outcome in which there's not. Such would mean
any red filament starting at left margin never reaches
right margin, and any black filament starting at top margin
never reaches lower margin.
If red filament from left margin never reaches right, where does
it go ? Either to top or bottom, or just ends in middle.
If it ends in middle, it does so only by abutting black filament,
for which same discussion can be made.
So let's just consider red filament that goes only to top or bottom.
There's a symmetry here, so we'll just consider red filament that
goes from left to top.
If filament is a long diagonal, red has won, so assume it starts
somewhere in middle of left side. Hence there are black tiles
below it.
O.K. you continue. Again, I sure wish this conferencing system
let us DRAW PICTURES ! How can we run a conference without
audio visual aides ? Particularly a math conference! We sure
are in the dark ages . . .
/Eric
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| 517.2 | no draw -> 1st player wins | MODEL::YARBROUGH | Wed Jun 18 1986 16:09 | 4 | |
Having proved that the game cannot end in a draw, you can now prove
that the first player has a winning strategy, since any hypothetical
second-player win can be converted into a first-player win by making
a random move (which can only help).
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