## 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

dvgrn wrote:Huh. It looked pretty good. How about 49?

x = 13, y = 14, rule = LifeHistory10.2A$5.2A3.A$5.C2.C.C$6.CA.C$7.C$5.C2.2ACA$5.CA.A3.C$6.C.A2.2A$6.C.2A$3.AC.C.C$4.A.A2.C$.A2C2.C3.C$A2.C.A5.A$2A2.A5.CA! The top can be reduced, so 48: x = 13, y = 13, rule = LifeHistory5.2A2.2A$5.C2.C.C$6.CA.C$7.C$5.C2.2ACA$5.CA.A3.C$6.C.A2.2A$6.C.2A$3.AC.C.C$4.A.A2.C$.A2C2.C3.C$A2.C.A5.A$2A2.A5.CA! An alternative 48: x = 13, y = 13, rule = LifeHistory5.2A2.2A$5.C2.C.C$6.CA.C$7.C$5.C2.2ACA$5.CA.A3.C$6.C.A2.2A$6.C.2A$2A.AC.C.C$A3.A.A2.C$.A2C2.C3.C$3.C.A5.A$4.A5.CA! Things to work on: - Find a (7,1)c/8 ship in a Non-totalistic rule (someone please search the rules) - Find a C/10 in JustFriends - Find a C/10 in Day and Night AforAmpere Posts: 1003 Joined: July 1st, 2016, 3:58 pm ### Re: Solitaire of Life The previous problem has one 31-cell solution within a 16-by-16 bounding box (probably less). I found this out using WinLifeSearch. 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: 723
Joined: May 30th, 2016, 8:47 pm
Location: Milky Way Galaxy: Planet Earth

### Re: Solitaire of Life

Gamedziner wrote:The previous problem has one 31-cell solution within a 16-by-16 bounding box (probably less). I found this out using WinLifeSearch.

31 cells? Yikes. It's good to have a target, but so far I can only get to 34:

x = 10, y = 12, rule = LifeHistory2A$C2.CA$2.2C.A$5.C$2.AC.A.C$2.A.C.A.C$6.A2.A$AC3AC2.AC$C2.C$8.2C$7.C.A$8.A! dvgrn Moderator Posts: 5634 Joined: May 17th, 2009, 11:00 pm Location: Madison, WI ### Re: Solitaire of Life dvgrn wrote: Gamedziner wrote:The previous problem has one 31-cell solution within a 16-by-16 bounding box (probably less). I found this out using WinLifeSearch. 31 cells? Yikes. What makes it worse is that there are no other 31-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: 723
Joined: May 30th, 2016, 8:47 pm
Location: Milky Way Galaxy: Planet Earth

### Re: Solitaire of Life

AforAmpere wrote:The top can be reduced, so 48:
x = 13, y = 13, rule = LifeHistory5.2A2.2A$5.C2.C.C$6.CA.C$7.C$5.C2.2ACA$5.CA.A3.C$6.C.A2.2A$6.C.2A$3.AC.C.C$4.A.A2.C$.A2C2.C3.C$A2.C.A5.A$2A2.A5.CA!

Easy reduction to 47:
x = 13, y = 13, rule = LifeHistory5.2A2.A$5.C2.C.C$6.CA.C$7.C$5.C2.2ACA$5.CA.A3.C$6.C.A2.2A$6.C.2A$3.AC.C.C$4.A.A2.C$.A2C2.C3.C$A2.C.A5.A$2A2.A5.CA!
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$8.2A! Gamedziner Posts: 723 Joined: May 30th, 2016, 8:47 pm Location: Milky Way Galaxy: Planet Earth ### Re: Solitaire of Life Gamedziner wrote: dvgrn wrote: Gamedziner wrote:The previous problem has one 31-cell solution within a 16-by-16 bounding box (probably less). I found this out using WinLifeSearch. 31 cells? Yikes. What makes it worse is that there are no other 31-cell solutions. ...which I wasn't actually expecting to find, given I couldn't get lower than 36 at first: x = 11, y = 11, rule = LifeHistory2A$C2.C$2.2C$3.A.C$3.C.2AC$4.C3.C$5.A2.A$AC.A.C3.CA$CA.CA5.A$7.A2C$7.C! Thanks for the inspiration, dvgrn. I'll hold off on submitting since people appear to still be working on the bump. For reference, I also have a 47-cell solution to that one, although Gamedeziner's looks much more conducive to reduction in the top right: x = 12, y = 15, rule = LifeHistory7.2A$6.A2.A$3.AC2.C.C$3.A.CA.C$6.C.A.A$4.CA3.C.A$4.C5.AC$5.C$3.A.C$.2AC.CAC$A7.C$.2C.AC.A.C$2.C.A3.A.A$2.A.A4.C$3.A! EDIT: Yup, there it is: x = 13, y = 13, rule = LifeHistory5.2A2.A$5.C2.C.C$6.CA.C$7.C.A.A$5.C4.C.A$5.CA4.AC$6.C$6.C.2A$3.AC.C.C$4.A.A2.C$.A2C2.C3.C$A2.C.A5.A$2A2.A5.CA! 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 Gamedziner wrote: dvgrn wrote: Gamedziner wrote:The previous problem has one 31-cell solution within a 16-by-16 bounding box (probably less). I found this out using WinLifeSearch. 31 cells? Yikes. What makes it worse is that there are no other 31-cell solutions. A minor hint might be (select next line to see it). Think Aircraft Carriers. dvgrn Moderator Posts: 5634 Joined: May 17th, 2009, 11:00 pm Location: Madison, WI ### Re: Solitaire of Life Here's a much easier one. Don't use scripts, please! I already found the smallest solution (at least, to my knowledge). x = 6, y = 3, rule = LifeHistory5.C$4C.C$5.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 ### Re: Solitaire of Life I doubt there is any smaller solution than 16: x = 7, y = 5, rule = LifeHistoryA2.A.CA$4C.C$5.C$2A3.2A$2A! Things to work on: - Find a (7,1)c/8 ship in a Non-totalistic rule (someone please search the rules) - Find a C/10 in JustFriends - Find a C/10 in Day and Night AforAmpere Posts: 1003 Joined: July 1st, 2016, 3:58 pm ### Re: Solitaire of Life AforAmpere wrote:I doubt there is any smaller solution than 16: x = 7, y = 5, rule = LifeHistoryA2.A.CA$4C.C$5.C$2A3.2A$2A! There actually is, though. I'm hoping someone finds a 15-cell solution, because I couldn't come up with one. Didn't use a search program, though, as requested. dvgrn Moderator Posts: 5634 Joined: May 17th, 2009, 11:00 pm Location: Madison, WI ### Re: Solitaire of Life 14 cells: x = 7, y = 5, rule = LifeHistoryA2.A.CA$4C.C$5.C$2.3A$2.A! gmc_nxtman Posts: 1147 Joined: May 26th, 2015, 7:20 pm ### Re: Solitaire of Life gmc_nxtman wrote:14 cells: x = 7, y = 5, rule = LifeHistoryA2.A.CA$4C.C$5.C$2.3A$2.A! I won't ever say what exactly I get when using WLS for this, unless it is requested. Since Hdjensofjfnen requested that no one should use scripts, I will not reveal the patterns I found even upon others' request. With that caveat in mind, I can confirm that this is an optimal solution. There is one more optimal solution (excluding flipping along the x-axis). 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: 723
Joined: May 30th, 2016, 8:47 pm
Location: Milky Way Galaxy: Planet Earth

### Re: Solitaire of Life

Gamedziner wrote:
gmc_nxtman wrote:14 cells:

x = 7, y = 5, rule = LifeHistoryA2.A.CA$4C.C$5.C$2.3A$2.A!
I won't ever say what exactly I get when using WLS for this, unless it is requested. Since Hdjensofjfnen requested that no one should use scripts, I will not reveal the patterns I found even upon others' request.
With that caveat in mind, I can confirm that this is an optimal solution. There is one more optimal solution (excluding flipping along the x-axis).

x = 7, y = 5, rule = LifeHistoryA2.A.CA$4C.C$5.C$2.A.A$2.2A!
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: 1809
Joined: September 13th, 2014, 5:36 pm
Location: 0x-1

### Re: Solitaire of Life

Gamedziner wrote:
gmc_nxtman wrote:14 cells:

x = 7, y = 5, rule = LifeHistoryA2.A.CA$4C.C$5.C$2.3A$2.A!
I won't ever say what exactly I get when using WLS for this, unless it is requested. Since Hdjensofjfnen requested that no one should use scripts, I will not reveal the patterns I found even upon others' request.
With that caveat in mind, I can confirm that this is an optimal solution. There is one more optimal solution (excluding flipping along the x-axis).

[Sniped by A for Awesome, whoops]
Yet Another Randomly-Generated Puzzle:
x = 12, y = 12, rule = LifeHistory7.C.3C$10.C$3.C.2C$2.C5.C$.C5.2C2.C$6.C$10.C2$C9.C$10.C$2.C$C.C!
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

x = 12, y = 12, rule = LifeHistory7.C.3C$10.C$3.C.2C$2.C5.C$.C5.2C2.C$6.C$10.C2$C9.C$10.C$2.C$C.C!

My best so far is 49:
x = 16, y = 16, rule = LifeHistory9.2A$9.2A2$7.ACA3C$3.2A.A4.C.A$2.A.C.2CA5.A$.A.C5.C5.A$2.C5.2C2.C2A$7.C4.A$8.3AC2$.C8.AC$A.A7.AC$A2.C$.C.C$2.A! Things to work on: - Find a (7,1)c/8 ship in a Non-totalistic rule (someone please search the rules) - Find a C/10 in JustFriends - Find a C/10 in Day and Night AforAmpere Posts: 1003 Joined: July 1st, 2016, 3:58 pm ### Re: Solitaire of Life A new puzzle: x = 9, y = 13, rule = LifeHistory3.C.C2$C3.C3.C$2.C3.C3$.C2.C2.C3$2.C3.C$C3.C3.C2$3.C.C! Things to work on: - Find a (7,1)c/8 ship in a Non-totalistic rule (someone please search the rules) - Find a C/10 in JustFriends - Find a C/10 in Day and Night AforAmpere Posts: 1003 Joined: July 1st, 2016, 3:58 pm ### Re: Solitaire of Life 53 cells: x = 11, y = 15, rule = LifeHistory5.A$2A2.C.C$A2.A2.A$.C.A.C3.CA$2.AC.A.C2.A$5.A.2A$2.2A.A$2.CA.C.AC$5.A.2A$2.2A.A$A2.C.A.CA$AC3.C.A.C$4.A2.A2.A$4.C.C2.2A$5.A! EDIT: 51: x = 11, y = 15, rule = LifeHistory5.A$3.ACACA$2.A5.A$.C.A.CA2.C$.A.CA.ACA$2A$2.A.2A.2A$2.CA.C.AC3$3.CA.AC.2A$.C2.AC.A.CA$.2A$3.ACAC$3.A2.A! EDIT: 50: x = 10, y = 15, rule = LifeHistory2.A2.A$2.ACAC$2A$C2.AC.A.C$2.CA.ACA.A$9.A$.A.2A.A.A$.CA.C.AC3$2.CA.AC.2A$C2.AC.A.CA$2A$2.ACAC$2.A2.A! gmc_nxtman Posts: 1147 Joined: May 26th, 2015, 7:20 pm ### Re: Solitaire of Life 46? x = 9, y = 15, rule = LifeHistory4.A$2.ACACA$.A5.A$C2.AC.A.C$.AC.A.CA2$.2A.A.2A$.C.AC.AC3$.AC.A.CA$C2.AC.A.C$.A5.A$2.ACACA$4.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

x = 9, y = 15, rule = LifeHistory4.A$2.ACACA$.A5.A$C2.AC.A.C$.AC.A.CA2$.2A.A.2A$.C.AC.AC3$.AC.A.CA$C2.AC.A.C$.A5.A$2.ACACA$4.A! Not an optimal solution. 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: 723
Joined: May 30th, 2016, 8:47 pm
Location: Milky Way Galaxy: Planet Earth

### Re: Solitaire of Life

Since it has been a full week, I'll give a hint: an optimal solution exists with 43 cells.
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: 723 Joined: May 30th, 2016, 8:47 pm Location: Milky Way Galaxy: Planet Earth ### Re: Solitaire of Life gmc_nxtman wrote:14 cells: x = 7, y = 5, rule = LifeHistoryA2.A.CA$4C.C$5.C$2.3A$2.A! Correct, that was my solution. 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 Here's a new puzzle, if anyone wants one: x = 12, y = 10, rule = LifeHistory2C3.C$4.C.C$3.C.C$3.C.C.C$2.C3.C$2.C5.C$3.C6.C$.C3.C5.C$6.C4.C$5.C!

77topaz

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

43 cells:

x = 13, y = 10, rule = LifeHistory.2C3.C$2.A2.C.C$2.A.C.C$.2A.C.C.C$3.C.A.C.A$3.C.A.A.C$.2A.C.A.A.AC$2.C3.C3.A.C$A.A2.A.C2.A.C$2A4.C4.A! EDIT: 40: x = 12, y = 13, rule = LifeHistory2A$2C3.C$4.C.C$3.C.C$3.C.C.C$.AC.A.C.A$A.C.A3.C$A2.C.A2.2AC$.C.A.C5.C$2.A2.AC3.AC$5.C$7.A$6.2A! gmc_nxtman Posts: 1147 Joined: May 26th, 2015, 7:20 pm ### Re: Solitaire of Life Alternative 40 x = 12, y = 12, rule = LifeHistory2C3.C$.A2.C.C$.A.C.C$2A.C.C.C$2.C.A.C.A$2.C.A3.C$3.C.A2.2AC$.C.A.C5.C$.2A2.AC3.AC$5.C$7.A$6.2A!
Sarp

Posts: 193
Joined: March 1st, 2015, 1:28 pm

### Re: Solitaire of Life

38:
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!
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]