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Below is an initial state for Conway's Game of Life with a single pulsar. Living cells are white.

enter image description here

The area marked with red is your base. You are free to modify any of the red cells, but only those, and only in the initial generation. You are not allowed to do anything once the simulation starts.

Your goal is to annihilate every living cell in the grid – in other words, the game must reach a generation where every cell is dead, even in your base. Yet in other, way cooler words:

You have to construct a rocket to destroy the Sun and everything that was created in the process.

The grid is infinite in every direction, i. e. runaway gliders still count as living.

You may use a brute force algorithm if you really wish, but I don't recommend you to. For one thing, you're up against the halting problem. Besides, finding a good construction all by yourself is fun (at least it was for me).

What I do recommend is downloading a good GoL simulator – solving this with only a paper and a pencil is probably not so much fun.

EDIT: The puzzle has been solved, but please don't be discouraged from posting alternative solutions. They are still very valuable, as they seem hard to come up with.

This puzzle has a continuation, created by kamenf.

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    $\begingroup$ Once this puzzle is solved, I will show you my original solution, codenamed "The Dalek". That is, if someone doesn't come up with the exact same solution. $\endgroup$ – BaSzAt Apr 20 '16 at 20:43
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    $\begingroup$ Even if we restrict ourselves to symmetric solutions, the search space is $2^{30}\approx 1\,000\,000\,000$, juuuust too large for brute-force search. Maybe a genetic algorithm would be more appropriate =) $\endgroup$ – 2012rcampion Apr 20 '16 at 21:04
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    $\begingroup$ The suggestion of a genetic algorithm was more of a joke, since both it and the game of life are associated with evolution. Personally I'd just brute-force in order of increasing population, and hope that the solution is sparse... $\endgroup$ – 2012rcampion Apr 20 '16 at 21:16
  • $\begingroup$ @2012rcampion I'd still be happier if you found one manually. I'm sure the CPU you got from your parents isn't half as bad as the one you're sitting in front of. (I meant it the good way!!) $\endgroup$ – BaSzAt Apr 20 '16 at 21:22
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    $\begingroup$ @BaSzAt good point(s). Our sister site PPCG has the [popularity-contest] tag, where the accepted/winning answer is decided by votes at a certain deadline. That could be appropriate here. Anyway I feel that maybe you have accepted an answer a little soon: this could discourage others from posting solutions. $\endgroup$ – Oliphaunt Apr 21 '16 at 7:07

10 Answers 10

73
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The following is a solution with 34 generations:

enter image description here enter image description here

And, yes, it was really fun to play with it :).

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    $\begingroup$ Beautiful! And you solved it really fast! By the way, it's a different construction from mine. What do you name it? : ) $\endgroup$ – BaSzAt Apr 21 '16 at 6:31
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    $\begingroup$ Let call it "T-Ship". I was fast because I had enough clues - limiting area and I searched for something like ship. This one has two boosters, which in fact produces a lot of fire on ignition ;) $\endgroup$ – kamenf Apr 21 '16 at 12:03
  • $\begingroup$ Nice animation! May I invite you to add animations to the other answers, if you're so inclined? (Or perhaps post instructions... "Give a man a fish...") $\endgroup$ – Oliphaunt Apr 21 '16 at 15:49
  • $\begingroup$ @Oliphaunt On Windows or Mac the easiest way is to use tool like cockos.com/licecap which directly captures screen area to GIF $\endgroup$ – kamenf Apr 21 '16 at 17:14
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I found a sun destroyer with just 10 cells filled!

enter image description here

It takes 39 generations.

As animation:

enter image description here

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    $\begingroup$ Brilliant! If this were code golf, you would be the absolute winner! Thanks for posting it. $\endgroup$ – BaSzAt Apr 21 '16 at 10:48
  • $\begingroup$ Apparently, you can't do spoiler code blocks. I made a little edit. Hope you don't mind : ) $\endgroup$ – BaSzAt Apr 21 '16 at 10:54
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    $\begingroup$ NP. And welcome to Puzzling SE! (God, I've always wanted to say that) $\endgroup$ – BaSzAt Apr 21 '16 at 11:07
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    $\begingroup$ Brilliant first answer! $\endgroup$ – Oliphaunt Apr 21 '16 at 15:46
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6 cells, 43 and 50 generations

I found 11 unique (up to reflection) 6-cell solutions:

enter image description here

By the first generation of evolution, they form two identical groups:

  • The first, fourth, and last two patterns work by the same method as my previous answer, but are three generations (one pulsar period) slower. Except for some self-destructing debris they are the same after 17 generations.

  • The second group is initially the same as the first group, delayed by one generation. This group initially interacts with the pulsar much more quickly (at generation 21).

One thing that's notable is that they are all asymmetric, and stay asymmetric for 20 generations (unlike my initial solution which became symmetric on the first generation). Here's an animation comparing the two groups of 6-cell solutions:

enter image description here

previous solution: 7 cells, 40 generations

enter image description here

There are no solutions with fewer than 6 cells (that stabilize within 1000 generations).

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23 cells, 41 generations, humorous answer

Sorry, I couldn't resist it... The pulsar dies on "magical command" after 41 generations but it takes 23 initial cells.

I apologise for the crudeness of the image. It's my first time using Golly.

Pulsar dies on command

EDIT: The next challenge is answered under my registered name Ruutsa

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  • $\begingroup$ This one has an independent value on its own even if one didn't know what the original puzzle was. $\endgroup$ – BaSzAt Apr 22 '16 at 5:33
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    $\begingroup$ Sorry, but I did not get the humor? $\endgroup$ – Byte Commander Apr 22 '16 at 6:09
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    $\begingroup$ @ByteCommander Rotate the screen by 90°. $\endgroup$ – BaSzAt Apr 22 '16 at 6:09
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    $\begingroup$ Ah, now I see the "DIE" spell... Nice! :D $\endgroup$ – Byte Commander Apr 22 '16 at 6:11
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    $\begingroup$ You can request an account merge. (puzzling.stackexchange.com/help/merging-accounts) $\endgroup$ – wythagoras Apr 24 '16 at 18:54
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In case anyone is wondering, here is my own solution, which takes 38 generations.

enter image description here

(NB: When I made this puzzle, I had no idea if it's even generally solvable. It took me 4 or 5 hours, while having the freedom to change the drawing area as I like.)

By the way, the bottom cells are just for decoration. The following works too:

enter image description here

As animation:

enter image description here

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  • $\begingroup$ For sure this one looks a lot better then mine :) $\endgroup$ – kamenf Apr 21 '16 at 12:11
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    $\begingroup$ @Oliphaunt 38 generations $\endgroup$ – kamenf Apr 21 '16 at 15:51
  • $\begingroup$ Is that a picture of a Dalek from Doctor Who? Nice! $\endgroup$ – Byte Commander Apr 22 '16 at 6:08
  • $\begingroup$ EX-TER-MIN-ATE! $\endgroup$ – David Conrad Apr 26 '16 at 2:55
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I made another one, with a mere 8 cells. It takes 44 generations.

enter image description here

As animation:

enter image description here

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More humorous solutions (destroy methods)

Sorry, I couldn't resist too

Call 911 :) 20 cells, 38 generations:

enter image description here

Use AI (artificial intelligence), 62 generations:

enter image description here

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    $\begingroup$ This is fantastic :) $\endgroup$ – 6005 Apr 24 '16 at 23:40
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23 cells, 41 generations, humorous answer 2: a special word?

It seems to be a special word. When said whimsically it moves stars. When said in annoyance it destroys them.

OH! - blue

Here's the animation

Pulsar - OH! - blue

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We have the smallest (6 cells), so to complete the picture here is (probably) the biggest "ship", 46 cells, 40 generations:

enter image description here

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    $\begingroup$ i saw a heart at 3rd gen. so i am upvoting <3 $\endgroup$ – nim Apr 26 '16 at 13:17
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I've come across something even better:

run this and you'll see why

:)

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    $\begingroup$ Great work, but could you include an animated image like the other posters? It's hard to see if it's a working answer with just a still shot. $\endgroup$ – feelinferrety May 6 '16 at 15:58

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