This file contains some manually-obtained results, including
manually-designed algorithms for a few cases.  All algorithms herein
have an implicit "if the bell doesn't ring" attached to each step.

W prime >3 and 2<=H<=W-2 suspected impossible.  Maybe even W odd >3 and
2<=H<=W-2.

W>2 H=W-1 borders on trivial.

W=2 H=1 - trivial.

W>2 H=1 - easily proved impossible.  (It is possible for every spin to
cause the single probe to miss the same two wells, which can be
different.)

W=4 H=2 - the standard pouzzle-book version.
2 patterns: XX-- X-X-
	XX--: Both down
	X-X-: Both down
	X-X-:
		If one up: invert it, ring
		If not: invert either
	XX--: Invert both
	X-X-: Invert both

W=5 H=2 - easily proved impossible; two cells *-*-- can be different
and fall into unprobed positions on every spin.
2 patterns: XX--- X-X--

W=5 H=2 - manually suspected impossible, computer search agrees
2 patterns: XXX-- XX-X-

W=6 H=3 - easily proved impossible; two cells *-*--- can be different
and fall into unprobed positions on every spin.
4 patterns: XXX--- XX-X-- XX--X- X-X-X-

W=6 H=4 - possible
3 patterns: XXXX-- XXX-X- XX-XX-
	XXXX--: all down
	XXX-X-: all down
	(Now have *-----)
	XXX-X-: if any u, invert it, ring
		if not, invert -*----
	(Now have *-*---)
	XXXX--: udud--: invert *-*---, ring
		dudu--: invert -*-*--, ring
		ddud--: invert *-----
		dddu--: invert -*----
		uddd--: invert --*---
		dudd--: invert ---*--
	(Now have *-*-*-)
	XXX-X-: invert *-*-*-, ring

W=7 H=3 - impossible, basically same proof as W=6 H=3
5 patterns: XXX---- XX-X--- XX--X-- XX---X- X-X-X--

W=7 H=4-5 - suspected impossible

W=8, H<4 - suspected impossible

W=8 H=4 - unsure
10 patterns: XXXX---- XXX-X--- XXX--X-- XXX---X- XX-XX--- XX-X-X-- XX-X--X- XX--XX-- XX--X-X- X-X-X-X-

W=8 H=5 - unsure
7 patterns: XXXXX--- XXXX-X-- XXXX--X- XXX-XX-- XXX-X-X- XXX--XX- XX-XX-X-

W=8 H=6 - possible
4 patterns: XXXXXX-- XXXXX-X- XXXX-XX- XXX-XXX-
	XXXXXX--: all down
	XXXXX-X-: all down
	(Now have *-------)
	XXXXX-X-: one u, invert it, ring
		no u: invert ------*-
	(Now have **------)
	XXXXXX--: all d, invert all, ring
		two u, invert them, ring
		uddddd--: invert *--*----
		dddddu--: invert --*--*--
	(Now have *---*---)
	XXX-XXX-: if two u, invert them, ring
		else, invert all, ring

W=9 H=6 - unsure
10 patterns: XXXXXX--- XXXXX-X-- XXXXX--X- XXXX-XX-- XXXX-X-X- XXXX--XX- XXX-XXX-- XXX-XX-X- XXX-X-XX- XX-XX-XX-

W=9 H=7 - possible
4 patterns: XXXXXXX-- XXXXXX-X- XXXXX-XX- XXXX-XXX-
	XXXXXXX--: all down
	XXXXXX-X-: all down
	(Now have *--------)
	XXXXXX-X-: one u, invert it, ring
		no u: invert -------*-
	(Now have **-------)
	XXXXXX-X-: two u: invert them, ring
		uddd-ddd-: invert --*--*---
		dddu-ddd-: invert -*-*---*-
		dddd-udd-: invert -*---*-*-
		dddd-ddu-: invert --*--*-*-
	(Now have udduddudd)
	XXXXX-XX-: if three u, invert them, ring
		else invert all d, ring