| The easier half of the problem. Forget about the precise position
of the kings at the moment, and label some of the squares on the board.
+--+--+--+--+--+--+--+--+
| | i| j| k| l| m| n| |
+--+--+--+--+--+--+--+--+
| | b| c| d| e| f| g| |
+--+--+--+--+--+--+--+--+
| | a| |BP| | | h| |
+--+--+--+--+--+--+--+--+
|BP| | |WP| |BP| | |
+--+--+--+--+--+--+--+--+
|WP| | a|WP| |WP| | h|
+--+--+--+--+--+--+--+--+
| b| c| b| c| d| e| f| g|
+--+--+--+--+--+--+--+--+
| i| j| i| j| k| l| m| n|
+--+--+--+--+--+--+--+--+
| b| c| b| c| d| e| f| g|
+--+--+--+--+--+--+--+--+
Whenever the White king moves, the Black king should move to the square of the
same label. Since the mapping from the White king's orbit to the Black's
preserves adjacency, the Black king can alway do this. Whenever the White
king is at a or h, the Black king prevents him from penetrating Black lines.
So to start this up, the Black king must move to b7, and draws.
Andrew
|
| Your labels are different than the ones I used. :-) After
noting the key points b5 and h5 and the corresponding squares,
the win I had come up with White to move looked like
1. Kb1, Ka8 or Ka6 2. Kb2, Ka7 3. Kb3, resigns :-)
and at the end, or if black varies earlier, the correspondence
is broken (and so White can force through to either b5 or h5).
For example, if White moves to d3 (labelled c) when Black is
already at c7 (also labelled c), then Black must either fall
back out of reach of b6 (then White moves to c4 and next b5)
or move to the b file (then White races to h5).
Examples if Black varies early are 1. Kb1, Kb6. 2. Kc2 and
if Black moves to a square with a 'b' or 'c' label then White
does the same. If Black retreats to the a file then White
reaches h5. But those are all of Black's choices. For example,
2. ..., Kb7 3. Kb3 and if Black drops to the 8th rank or goes
to b6 then White plays to c4 and b5 next move; otherwise Black
moves to c7 and White to d3 (see previous paragraph).
How to win after White plays to h5 with Black on the f file
is left to the reader. :-)
Dan
|