Spoiler for What area can you vacate?
1
1
01 can vacate bottom left square
1
01
01
11
001
01
11
011
001 can vacate immediate neighbors of bottom left square
01
101
011
001
011
1001
011
001
011
1011
0101
001
011
1111
0011
001 can vacate 2x2 area
So the best you can do is
00
00
or
0
0
...
0
0
000...00
1
1
01 can vacate bottom left square
1
01
01
11
001
01
11
011
001 can vacate immediate neighbors of bottom left square
01
101
011
001
011
1001
011
001
011
1011
0101
001
011
1111
0011
001 can vacate 2x2 area
Spoiler for More futility
It may be easier with my other formulation of the problem.
I'll try and vacate
0
00
00
1
1
01
1
02
001
12
002
001
1
03
002
001 notice the 2 and the 3...
12
013
0011
001 notice that the 2 and the 3 swapped relative positions...
01
113
0112
0011
001 the 2 and the 3 swapped again. They'll continue to swap, and will never finish.
So it isn't possible to vacate that area.
It may be easier with my other formulation of the problem.
I'll try and vacate
0
00
00
1
1
01
1
02
001
12
002
001
1
03
002
001 notice the 2 and the 3...
12
013
0011
001 notice that the 2 and the 3 swapped relative positions...
01
113
0112
0011
001 the 2 and the 3 swapped again. They'll continue to swap, and will never finish.
So it isn't possible to vacate that area.
So the best you can do is
00
00
or
0
0
...
0
0
000...00
Spoiler for second one
1
1
01
1
01
01
11
001
01
11
011
001
01
101
011
001
11
011
011
001
111
0101
011
001
111
0111
0101
001
111
0111
0111
0001
001
1101
0111
0111
0001
011
1011
0111
0111
0001
111
0111
0111
0111
0001
1111
01101
0111
0111
0001
1111
01111
01101
0111
0001
1111
01111
01111
01101
0001
1111
01111
01111
01111
00001
etc.
1
01
1
01
01
11
001
01
11
011
001
01
101
011
001
11
011
011
001
111
0101
011
001
111
0111
0101
001
111
0111
0111
0001
001
1101
0111
0111
0001
011
1011
0111
0111
0001
111
0111
0111
0111
0001
1111
01101
0111
0111
0001
1111
01111
01101
0111
0001
1111
01111
01111
01101
0001
1111
01111
01111
01111
00001
etc.





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