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They are immortal and they are killing us. We may not be able to kill them, but we might be able to keep them occupied, distracted, for eternity. But we need to figure out how. Before there are no more of us.


In an arena that measures 25 by 25, play Conway's Game of Life with these additional rules:

  • Cells outside the arena are always dead.
  • The cell at the center of the arena cannot be occupied and is considered always dead.
  • You may designate additional cells in the arena that are always dead.
  • At the end of an iteration, if there are any live cells in the center 3x3 area (trigger zone), all cells in the center 5x5 area (kill zone) die.

Task: Create an arrangement that represents the start of a time-wise loop (i.e.: returns to its original arrangement after some number of iterations).

Scoring: Total number of cells killed in the trigger zone during the span of one loop times 125,000 divided by the number of iterations in the loop. Highest score wins. (Give your arrangement, the number of iterations in its loop, the number of cells killed that count towards your score for the loop, and your score. I'd also like to hear how you went about conceiving of your arrangement.)

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  • $\begingroup$ What use is the 125000? $\endgroup$ – boboquack Sep 8 '17 at 0:28
  • $\begingroup$ @boboquack Sets the naive maximum score at one million. Otherwise, it'd be 8 and it's pretty unlikely anybody would get more than ~2. $\endgroup$ – Ouroborus Sep 8 '17 at 0:38
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    $\begingroup$ Two is still more than how many bitcoins I have. $\endgroup$ – John Dvorak Sep 8 '17 at 1:29
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    $\begingroup$ If anyone cares, I made a Processing sketch you can play with for these rules. See the instructions by pressing the i-button at the top. I couldn't come up with a solution yet, though :) $\endgroup$ – R.M Dec 21 '17 at 22:15
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EDIT: The sketch's scoring is now fixed. I will keep the answer as it is because I think optimizing for its prior method of scoring is also an interesting question.

The Processing sketch in @R.M.'s comment on the question itself gave me a score of 312500 for this arrangement:


Arrangement of cells

but I calculate its score to be lower — 187500 — as I believe the sketch is counting kills within the larger kill zone that are not within the trigger zone toward the total score, contrary to the question.

What I believe to be the theoretical maximum scores would be 250000 for the what seems to be actual scoring system and 916666.666... for the sketch's scoring system — the maximum number of cells that can ever occupy the trigger zone at once is six, the maximum number of cells that can ever occupy the kill zone at once should be twenty-two, and the minimum period between iterations during which kills occur is 3, as information cannot travel faster than one cell per iteration inward.

Note that this pattern is a variant of the emulator family of oscillators. It has a period of 4, like the others in the family. There are 6 cells killed within the trigger zone and 10 total per cycle. There are no permanently dead cells (other than the central cell) in my answer. I found this using my own intuition and prior knowledge of Conway's Game of Life, not with an automated search. It should be possible to set up an automated search for period 3 configurations that could approach or even meet the maximum scores, but I don't have the time to do so myself.

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  • $\begingroup$ Thanks for pointing that out! I have now fixed the scoring system. $\endgroup$ – R.M Apr 3 '18 at 14:00
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    $\begingroup$ Nice answer. I wish @R.M. would have an anser to upvote on as well. Greate to have somebody putting in the effort for others to enjoy. Without a "testground" the puzzle would be much much less attractive. $\endgroup$ – BmyGuest Apr 12 '18 at 5:56

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