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added 10 characters in body
Source Link
Saúl RM
  • 10.6k
  • 2
  • 28
  • 48

With $5$ you can using the following moves:

.....  .....  .....  .....  .....  .....  .....  ..oo.  ...oo 
.....  ..o..  ..o..  ..o..  ..oo.  ...oo  ..ooo  ..ooo  ..ooo 
.oo..  .oo..  .oo..  ..oo.  ..oo.  ..oo.  ..oo.  .....  ..... 
ooo..  oo...  .oo..  ..oo.  ..o..  ..o..  .....  .....  ..... 

So the only numbernumbers of pieces for which no configuration can go to infinity isare $1$ and $3$.

With $5$ you can using the following moves:

.....  .....  .....  .....  .....  .....  .....  ..oo.  ...oo 
.....  ..o..  ..o..  ..o..  ..oo.  ...oo  ..ooo  ..ooo  ..ooo 
.oo..  .oo..  .oo..  ..oo.  ..oo.  ..oo.  ..oo.  .....  ..... 
ooo..  oo...  .oo..  ..oo.  ..o..  ..o..  .....  .....  ..... 

So the only number of pieces for which no configuration can go to infinity is $3$.

With $5$ you can using the following moves:

.....  .....  .....  .....  .....  .....  .....  ..oo.  ...oo 
.....  ..o..  ..o..  ..o..  ..oo.  ...oo  ..ooo  ..ooo  ..ooo 
.oo..  .oo..  .oo..  ..oo.  ..oo.  ..oo.  ..oo.  .....  ..... 
ooo..  oo...  .oo..  ..oo.  ..o..  ..o..  .....  .....  ..... 

So the only numbers of pieces for which no configuration can go to infinity are $1$ and $3$.

added 99 characters in body
Source Link
Saúl RM
  • 10.6k
  • 2
  • 28
  • 48

With $5$ you can using the following moves:

...
 ..  .
oo.
ooo
...
oo  .
 ....  .....  .....  .....  .....  ..oo.  ...oo 
.....  ..o
 ..  .
 .o..  ..o..  ..oo.
   ...oo
   ..o
ooo  ..ooo  .
 .ooo 
.oo
 ..  .
 oo..  .oo
ooo
..  .
 .oo.  .
 .oo.  ..oo.  ..oo.  .....  ..... 
ooo
 ..  oo...
   .oo..  ..oo.  ..o..  ..o..  .....  .....  ..... 

So the only number of pieces for which can'tno configuration can go to infinity is $3$.

With $5$ you can using the following moves:

...
 ...
oo.
ooo
...
oo.
 oo.
..o
 ...
 oo.
 .oo
 ..o
...
 ooo
.oo
 ...
 .oo
ooo
...
 ...
 oo.
ooo
 ...
 ...

So the only number of pieces which can't go to infinity is $3$.

With $5$ you can using the following moves:

.....  .....  .....  .....  .....  .....  .....  ..oo.  ...oo 
.....  ..o..  ..o..  ..o..  ..oo.  ...oo  ..ooo  ..ooo  ..ooo 
.oo..  .oo..  .oo..  ..oo.  ..oo.  ..oo.  ..oo.  .....  ..... 
ooo..  oo...  .oo..  ..oo.  ..o..  ..o..  .....  .....  ..... 

So the only number of pieces for which no configuration can go to infinity is $3$.

Source Link
Saúl RM
  • 10.6k
  • 2
  • 28
  • 48

With $5$ you can using the following moves:

...
...
oo.
ooo
...
oo.
oo.
..o
...
oo.
.oo
..o
...
ooo
.oo
...
.oo
ooo
...
...
oo.
ooo
...
...

So the only number of pieces which can't go to infinity is $3$.