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minor edit: better display
Sebastien Palcoux
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The 1-step vanishing polyplets on Conway's game of life

A $n$-polyplet is a collection of $n$ cells on a grid which are orthogonally or diagonally connected.
The number of $n$-polyplets is given by the OEIS sequence A030222: $1, 2, 5, 22, 94, 524, 3031, \dots$

See below the five $3$-polyplets:
enter image description here
A polyplet will be called $1$-step vanishing on Conway's game of life, if every cell dies after one step.
We observed that for $n\le 4$, a $n$-polyplet is $1$-step vanishing iff $n \le 2$.

We found $1$-step vanishing polyplets with $n=9, 12$, see below:
enter image description here
Question: Is there an other $1$-step vanishing $n$-polyplet with $n \le 12$?
If yes, what are they? (note that there are exactly $37963911$ $n$-polyplets with $n \le 12$).

We can build infinitely many $1$-step vanishing polyplets with such pattern, see below with $n=142$:
enter image description here

Bonus question: Are there $1$-step vanishing polyplets of an other kind?

Sebastien Palcoux
  • 27k
  • 5
  • 74
  • 186