## Solitaire of Life

A forum where anything goes. Introduce yourselves to other members of the forums, discuss how your name evolves when written out in the Game of Life, or just tell us how you found it. This is the forum for "non-academic" content.

### Re: Solitaire of Life

PTW, I need to participate later (I need to practice welding).

KittyTac

Posts: 533
Joined: December 21st, 2017, 9:58 am

### Re: Solitaire of Life

x = 12, y = 11, rule = LifeHistory2A$2C3.C$4.C.C$3.C.C$3.C.C.C$.AC3.C.A$A.C.2A2.C$A2.C2.3A.C$.CA2.C3.A.C$6.C2.A.C$5.CA3.A!

Congratulations, that is one of four optimal solutions.
x = 81, y = 96, rule = LifeHistory58.2A$58.2A3$59.2A17.2A$59.2A17.2A3$79.2A$79.2A2$57.A$56.A$56.3A4$27.A$27.A.A$27.2A21$3.2A$3.2A2.2A$7.2A18$7.2A$7.2A2.2A$11.2A11$2A$2A2.2A$4.2A18$4.2A$4.2A2.2A$8.2A! Gamedziner Posts: 724 Joined: May 30th, 2016, 8:47 pm Location: Milky Way Galaxy: Planet Earth ### Re: Solitaire of Life Heh, the original solution I'd devised for that was (mostly) symmetrical and had 52 cells; I hadn't expected asymmetrical solutions would be able to be so much smaller. x = 12, y = 10, rule = LifeHistory2C3.C3.2A$.A2.C.C2.A$.A.C.C.A.A$2A.C.C.C.2A$2.C.A.C.A$2.C.A.A.C$2A.C.A.A.AC$.C.A.C.A.A.C$.A2.A.C2.A.C$2A3.C3.2A!

But now, a sort of reverse-Solitaire question can be asked: what is the smallest "challenge" pattern so that this 52-cell pattern is an optimal solution?

77topaz

Posts: 1345
Joined: January 12th, 2018, 9:19 pm

### Re: Solitaire of Life

77topaz wrote:But now, a sort of reverse-Solitaire question can be asked: what is the smallest "challenge" pattern so that this 52-cell pattern is an optimal solution?

This 29-celler might be a good starting point:
x = 12, y = 10, rule = LifeHistory2C3.C3.2C$4.C.C$.C7.C$3.C.C.C$2.C3.C$4.C3.C$3.C.C.C$.C7.C$4.C.C4.C$2C3.C3.2C! LifeWiki: Like Wikipedia but with more spaceships. [citation needed] BlinkerSpawn Posts: 1875 Joined: November 8th, 2014, 8:48 pm Location: Getting a snacker from R-Bee's ### Re: Solitaire of Life This 21 seems likely, haven't tested it with a computer yet x = 12, y = 10, rule = LifeHistoryAC3.C3.CA$.A2.A.A2.A$.A.C.C.A.A$CA.A.A.C.AC$2.C.C.A.A$2.A.A.C.C$CA.C.A.A.AC$.A.A.C.C.A.C$.A2.A.A2.A.A$AC3.C3.CA!
Sarp

Posts: 194
Joined: March 1st, 2015, 1:28 pm

### Re: Solitaire of Life

Sarp wrote:This 21 seems likely, haven't tested it with a computer yet
x = 12, y = 10, rule = LifeHistoryAC3.C3.CA$.A2.A.A2.A$.A.C.C.A.A$CA.A.A.C.AC$2.C.C.A.A$2.A.A.C.C$CA.C.A.A.AC$.A.A.C.C.A.C$.A2.A.A2.A.A$AC3.C3.CA! It doesn't work; there are multiple 51-cell solutions. x = 81, y = 96, rule = LifeHistory58.2A$58.2A3$59.2A17.2A$59.2A17.2A3$79.2A$79.2A2$57.A$56.A$56.3A4$27.A$27.A.A$27.2A21$3.2A$3.2A2.2A$7.2A18$7.2A$7.2A2.2A$11.2A11$2A$2A2.2A$4.2A18$4.2A$4.2A2.2A$8.2A!
Gamedziner

Posts: 724
Joined: May 30th, 2016, 8:47 pm
Location: Milky Way Galaxy: Planet Earth

### Re: Solitaire of Life

I am pretty sure I have found the optimal solution for this, although I'm not sure:
x = 3, y = 7, rule = LifeHistory.C$C$.C$C.C$.C$C$.C!
Life is hard. Deal with it.
My favorite oscillator of all time:
x = 7, y = 5, rule = B3/S2-i3-y4i4b3o$6bo$o3b3o$2o$bo!

Hdjensofjfnen

Posts: 1093
Joined: March 15th, 2016, 6:41 pm
Location: r cis θ

Hm...
x = 48, y = 48, rule = LifeHistory46.CA$45.A.A$44.C$43.A$42.C$41.A$40.C$39.A$38.C$37.A$36.C$35.A$34.C$33.A$32.C$31.A$30.C$29.A$28.C$27.A$26.C$25.A$24.C$24.2A3$20.CA$19.A.A$18.C$17.A$16.C$15.A$14.C$13.A$12.C$11.A$10.C$9.A$8.C$7.A$6.C$5.A$4.C$3.A$2.C$.A$C$2A! Life is hard. Deal with it. My favorite oscillator of all time: x = 7, y = 5, rule = B3/S2-i3-y4i4b3o$6bo$o3b3o$2o$bo! Hdjensofjfnen Posts: 1093 Joined: March 15th, 2016, 6:41 pm Location: r cis θ ### Re: Solitaire of Life Hdjensofjfnen wrote:I am pretty sure I have found the optimal solution for this, although I'm not sure: x = 3, y = 7, rule = LifeHistory.C$C$.C$C.C$.C$C$.C! 15? x = 6, y = 8, rule = LifeHistory5.A$3.C2A$2.C$A2.C$2AC.C$3.C$2.C$2.AC!

x = 6, y = 7, rule = LifeHistory3.CA$2.C2.A$A2.C.A$2AC.C$3.C$2.C$2.AC!
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$

http://conwaylife.com/wiki/A_for_all

Aidan F. Pierce

A for awesome

Posts: 1810
Joined: September 13th, 2014, 5:36 pm
Location: 0x-1

### Re: Solitaire of Life

A for awesome wrote:15?
x = 6, y = 8, rule = LifeHistory5.A$3.C2A$2.C$A2.C$2AC.C$3.C$2.C$2.AC! x = 6, y = 7, rule = LifeHistory3.CA$2.C2.A$A2.C.A$2AC.C$3.C$2.C$2.AC! I just did a search with WLS and determined that those were the only optimal solutions (excluding reflection). x = 81, y = 96, rule = LifeHistory58.2A$58.2A3$59.2A17.2A$59.2A17.2A3$79.2A$79.2A2$57.A$56.A$56.3A4$27.A$27.A.A$27.2A21$3.2A$3.2A2.2A$7.2A18$7.2A$7.2A2.2A$11.2A11$2A$2A2.2A$4.2A18$4.2A$4.2A2.2A$8.2A!
Gamedziner

Posts: 724
Joined: May 30th, 2016, 8:47 pm
Location: Milky Way Galaxy: Planet Earth

### Re: Solitaire of Life

Oh, yeah, you win by a whole lot. My solution was 21.
Life is hard. Deal with it.
My favorite oscillator of all time:
x = 7, y = 5, rule = B3/S2-i3-y4i4b3o$6bo$o3b3o$2o$bo!

Hdjensofjfnen

Posts: 1093
Joined: March 15th, 2016, 6:41 pm
Location: r cis θ

### Re: Solitaire of Life

This new puzzle is based on a still life that came up in an apgmera search today. Apparently it's a fairly rare still life, since there's only the one soup in Catagolue.

x = 14, y = 12, rule = LifeHistory14B$B12.B$B7.C.2C.B$B5.C4.C.B$B2.C4.C4.B$B2.2C.C6.B$B6.C.2C2.B$B4.C4.C2.B$B.C4.C5.B$B.2C.C7.B$B12.B$14B!#C Additional#C information#C you#C may#C not#C want:#C the#C source#C still#C life's#C apgcode#C starts#C with#C "xs34". With the additional restriction that all added cells have to be strictly inside the blue box, there's a unique solution. Without the blue box JLS finds four more possibilities. dvgrn Moderator Posts: 5634 Joined: May 17th, 2009, 11:00 pm Location: Madison, WI ### Re: Solitaire of Life [spoiler or something i guess] x = 10, y = 10, rule = LifeHistory4.2A$3.A2.C.2C$4.CA3.C$.C4.C2A$.2CAC$5.CA2C$.2AC4.C$C3.AC$2C.C2.A$4.2A!

gmc_nxtman

Posts: 1147
Joined: May 26th, 2015, 7:20 pm

### Re: Solitaire of Life

Missed by less than 30 secs
Sarp

Posts: 194
Joined: March 1st, 2015, 1:28 pm

### Re: Solitaire of Life

Isn't the solver supposed to keep the game going by supplying a new puzzle? Here's another small and probably easy one, with three minimal-population solutions:

Code: Select all
x = 10, y = 7, rule = LifeHistory2.C2.C$2.C2.C3.C$C8.C$C4.C$2.2C.C.C$2.C4.C$3.2C!

Adding one more white cell in any of the blue locations would make a puzzle with a unique smallest solution:

x = 10, y = 7, rule = LifeHistory2.C2.C$2.C2BC3.C$C3.B4.C$C4.C$2.2C.C.C$2.C4.C$3.2C!

dvgrn
Moderator

Posts: 5634
Joined: May 17th, 2009, 11:00 pm

### Re: Solitaire of Life

dvgrn wrote:Isn't the solver supposed to keep the game going by supplying a new puzzle?

At some point we kinda stopped doing that, for whatever reason.

31:
x = 11, y = 8, rule = LifeHistory4.2A$3.C2.C$3.C2.C2.AC$AC.2A.A.A.C$.C4.C.A$.A.2C.C.C$2A.C2.A.CA$4.2C! LifeWiki: Like Wikipedia but with more spaceships. [citation needed] BlinkerSpawn Posts: 1875 Joined: November 8th, 2014, 8:48 pm Location: Getting a snacker from R-Bee's ### Re: Solitaire of Life BlinkerSpawn wrote:31... Not minimal, but close! The 31-cell solution doesn't have a cell in any of the blue positions... dvgrn Moderator Posts: 5634 Joined: May 17th, 2009, 11:00 pm Location: Madison, WI ### Re: Solitaire of Life 30? x = 11, y = 8, rule = LifeHistory4.2A$3.C2.C$3.CBAC2.AC$AC.A.BA.A.C$AC.A2.C.A$3.2C.C.C$3.C2.A.CA$4.2C!
Sarp

Posts: 194
Joined: March 1st, 2015, 1:28 pm

Sarp wrote:30?
x = 11, y = 8, rule = LifeHistory4.2A$3.C2.C$3.CBAC2.AC$AC.A.BA.A.C$AC.A2.C.A$3.2C.C.C$3.C2.A.CA$4.2C! You got it. Somebody else's turn to make a puzzle... dvgrn Moderator Posts: 5634 Joined: May 17th, 2009, 11:00 pm Location: Madison, WI ### Re: Solitaire of Life x = 12, y = 8, rule = LifeHistory5.C$9.C$.C5.2C2.C$.C3.C3.C$C3.2C3.C$.C.C2.C$2.C6.C$4.2C!

gmc_nxtman

Posts: 1147
Joined: May 26th, 2015, 7:20 pm

### Re: Solitaire of Life

Here is a first attempt at a solution, 79 cells:
x = 17, y = 17, rule = LifeHistory2A$A8.2A$2.A.2A3.A2.A$.2A.A5.3A$.A3.A$2.3A.A3.3A$4.A.A2.C2.A$6.A.A.A2.CA$5.C.A.A.2C2.C$5.C3.C3.C.A$4.CA2.2C.2AC.2A$2.A2.C.C2.C$2.2A2.C.A2.A.C3A$8.2C2A.A2.A$7.A4.A$8.3A$10.2A!

EDIT: 71
x = 16, y = 16, rule = LifeHistory8.2A$2A.2A3.A2.A$.A.A5.3A$A3.A$.3A.A3.3A$3.A.A2.C2.A$5.A.A.A2.CA$4.C.A.A.2C2.C$4.C3.C3.C.A$3.CA2.2C.2AC.2A$.A2.C.C2.C$.2A2.C.A2.A.C3A$7.2C2A.A2.A$6.A4.A$7.3A$9.2A! wwei23 Posts: 935 Joined: May 22nd, 2017, 6:14 pm Location: The (Life?) Universe ### Re: Solitaire of Life [56, not 58]: x = 16, y = 12, rule = LifeHistory8.2A$6.C2.A$.A4.2A2.CA2.2A$A.C.2A2.2C2.C2.A$A.CA2.C3.C.2A$.C3.2C.2AC.A$2.CAC2.C4.A$3.C2.A2.ACA$.A3.2C.2A$.2A3.A$6.A.2A$7.A.A!

Much of the interior is forced by S3 in some form or other.
Last edited by BlinkerSpawn on October 7th, 2018, 10:44 pm, edited 1 time in total.
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

Posts: 1875
Joined: November 8th, 2014, 8:48 pm
Location: Getting a snacker from R-Bee's

### Re: Solitaire of Life

Not minimal.

EDIT: Is it just me, or does this game have conceptual similarities to minesweeper? When the interior is forced like in this particular puzzle, similar inferences have to be made to those made in minesweeper regarding what cells ("mines") are allowed to be where.

gmc_nxtman

Posts: 1147
Joined: May 26th, 2015, 7:20 pm

### Re: Solitaire of Life

gmc_nxtman wrote:EDIT: Is it just me, or does this game have conceptual similarities to minesweeper? When the interior is forced like in this particular puzzle, similar inferences have to be made to those made in minesweeper regarding what cells ("mines") are allowed to be where.

Total agreement there.
Down to 54:
x = 14, y = 12, rule = LifeHistory8.2A$6.C2.A$.A4.2A2.CA$A.C.2A2.2C2.C$A.CA2.C3.C.A$.C3.2C.2AC.2A$2.CAC2.C4.A$3.C2.A2.AC.A$.A3.2C.2A.A$.2A4.A$7.A.2A$8.A.A! Forcing diagram (red = forced-OFF, yellow = forced-ON): x = 14, y = 12, rule = LifeHistory8.2A$6.C2.A$.A4.2A2DCA$ADCD2A2.2CD.C$ADCE2DC3DC.A$.C3D2CD2AC.2A$.DCEC2DC4.A$.2DC2DED.AC.A$.A3D2CD2A.A$.2A4.A$7.A.2A$8.A.A!
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

Posts: 1875
Joined: November 8th, 2014, 8:48 pm
Location: Getting a snacker from R-Bee's

### Re: Solitaire of Life

Still not minimal. Also just so you know, this is a valid alternative forcing diagram:

x = 13, y = 8, rule = LifeHistory6.C$8.2DC$.DCDAD2.2CD.C$2DC3DC3DC$DCA2D2CD2.C$2DCDC2DC$A2DC6.C\$5.2C!

gmc_nxtman

Posts: 1147
Joined: May 26th, 2015, 7:20 pm

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