If the initial position of [Conway's game of life][1] is a line of $n \le 100$ cells, then it vanishes completely after some steps iff $n \in \{0,1,2,6,14,15,18,19,23,24 \}$. See below for $n=24$. [![enter image description here][2]][2] *Question*: Can we prove that such a vanishing is no more possible for $n>24$? [1]: https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life [2]: https://i.sstatic.net/dEo8p.gif