May 2015

Xyzzy · 2015-05-02, 14:16

http://domino.research.ibm.com/Comm/...s/May2015.html

TheMawn · 2015-05-02, 21:44

My work on this was going so well until I hit a big hiccup: Even though players can't START with more than 255 dollars, they can go higher than 255.

I created a list of all possible starting configurations (keeping in mind that the order does not matter so I had [1,4,6] but didn't keep [6,4,1] and [1,6,4] etc).

For any that contained duplicates, I tagged them as possibly ending on the first tun. For any that did not, I generated the three possible configurations that they could lead to and I was going to start working on the logic that if any of those three possibilities ended on turn 1, then the initial config ended on turn 2, and so on.

Unfortunately, for example, [32,254,255] can lead to [1,32,508] which is not in my list of possible configurations. I will need to think of something to deal with this. It is good to know that 508 is the largest amount any player can reach, but that still makes a shit load more configurations to deal with.

And yes, I AM trying to go for the full enchilada.

EDIT: I am going to need 64-bit excel to do this...

TheMawn · 2015-05-03, 01:19

As far as I can tell, it is not possible for two players to both be above 255 if they start at or below 255. I would like a counterexample if someone is only marginally interested in this problem.

I can't use words to make a proper sounding proof but I feel like I've tried everything.

science_man_88 · 2015-05-03, 01:38

Quote:

Originally Posted by TheMawn

As far as I can tell, it is not possible for two players to both be above 255 if they start at or below 255. I would like a counterexample if someone is only marginally interested in this problem.

I can't use words to make a proper sounding proof but I feel like I've tried everything.

this:

[253,254,255]->[253,508,1]->[506,255,1]->[505,255,2]->[503,255,4]->[499,255,8]->[491,255,16]->[475,255,32]->[443,255,64]->[379,255,128]->[251,255,256] (sped ahead originally from[506,255,1], not saying how right now)->[502,4,256] I believe is the path you mean ?

TheMawn · 2015-05-03, 02:58

Quote:

Originally Posted by science_man_88

this:

[253,254,255]->[253,508,1]->[506,255,1]->[505,255,2]->[503,255,4]->[499,255,8]->[491,255,16]->[475,255,32]->[443,255,64]->[379,255,128]->[251,255,256] (sped ahead originally from[506,255,1], not saying how right now)->[502,4,256] I believe is the path you mean ?

Well that's good to know. ... And also highly frustrating. Very good find, though, thanks!

I guess I have a bit of code to re-write. I suppose this also raises the question of whether two numbers > 256 is possible.

It looks like your non-brute-force insights into this problem are a bit better than mine, especially if you saw how to get from [506,255,1] to [502,4,256] in one big movement.

science_man_88 · 2015-05-03, 10:20

Quote:

Originally Posted by TheMawn

Well that's good to know. ... And also highly frustrating. Very good find, though, thanks!

I guess I have a bit of code to re-write. I suppose this also raises the question of whether two numbers > 256 is possible.

It looks like your non-brute-force insights into this problem are a bit better than mine, especially if you saw how to get from [506,255,1] to [502,4,256] in one big movement.

I came across the insights to go from [506,255,1] to [251,255,256] but those insights came from playing around and realizing something about it two of the values are constantly chosen.

science_man_88 · 2015-05-03, 12:21

Quote:

Originally Posted by TheMawn

I suppose this also raises the question of whether two numbers > 256 is possible

this:

[506,255,1]->->[506,0,256]->->[250,0,512]->->[500,0,262] if you allow 0 in the mix. ->-> is my way of saying fast forward to I guess.

science_man_88 · 2015-05-03, 13:58

I think I have an answer without my code. Well that seems like a waste.

0 makes at least 127 trivial answers if it's allowed at the start.

TheMawn · 2015-05-03, 15:15

Zero is impossible by the rules of the game. You would have to lose to someone who has the same amount of money as you, which is a game end.

science_man_88 · 2015-05-03, 15:28

Quote:

Originally Posted by TheMawn

Zero is impossible by the rules of the game. You would have to lose to someone who has the same amount of money as you, which is a game end.

I mean't at the start for those trivial answers. but yeah I forgot but I can tell you why this one would hit a 0 if left indefinitely have you figured out what I figured out about how to show each branch quickly ? I just don't seem to be able to code it for some reason.

TheMawn · 2015-05-03, 16:40

[506,255,1]->->[506,0,256]

This cannot legally happen. And this is clearly not a case where a player starts with zero.

You end up at [506,128,128] and you cannot get to [506,0,256] because the rules of the game state that if two players with equal amounts of money are matched up, then the game ends.

A player CANNOT end up with 0 dollars because they would have lost to someone with the same amount of money as them which ends the game. I don't know how else to say this.

2015-05-02, 14:16	#1
Xyzzy Aug 2002 3·43·67 Posts	May 2015 http://domino.research.ibm.com/Comm/...s/May2015.html

2015-05-02, 21:44	#2
TheMawn May 2013 East. Always East. 11×157 Posts	My work on this was going so well until I hit a big hiccup: Even though players can't START with more than 255 dollars, they can go higher than 255. I created a list of all possible starting configurations (keeping in mind that the order does not matter so I had [1,4,6] but didn't keep [6,4,1] and [1,6,4] etc). For any that contained duplicates, I tagged them as possibly ending on the first tun. For any that did not, I generated the three possible configurations that they could lead to and I was going to start working on the logic that if any of those three possibilities ended on turn 1, then the initial config ended on turn 2, and so on. Unfortunately, for example, [32,254,255] can lead to [1,32,508] which is not in my list of possible configurations. I will need to think of something to deal with this. It is good to know that 508 is the largest amount any player can reach, but that still makes a shit load more configurations to deal with. And yes, I AM trying to go for the full enchilada. EDIT: I am going to need 64-bit excel to do this... Last fiddled with by TheMawn on 2015-05-02 at 21:48

2015-05-03, 13:58	#8
science_man_88 "Forget I exist" Jul 2009 Dartmouth NS 2102₁₆ Posts	I think I have an answer without my code. Well that seems like a waste. 0 makes at least 127 trivial answers if it's allowed at the start. Last fiddled with by science_man_88 on 2015-05-03 at 14:30

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2015-05-03, 01:19	#3
TheMawn May 2013 East. Always East. 6BF₁₆ Posts	As far as I can tell, it is not possible for two players to both be above 255 if they start at or below 255. I would like a counterexample if someone is only marginally interested in this problem. I can't use words to make a proper sounding proof but I feel like I've tried everything.

2015-05-03, 15:15	#9
TheMawn May 2013 East. Always East. 11·157 Posts	Zero is impossible by the rules of the game. You would have to lose to someone who has the same amount of money as you, which is a game end.

2015-05-03, 16:40	#11
TheMawn May 2013 East. Always East. 11·157 Posts	[506,255,1]->->[506,0,256] This cannot legally happen. And this is clearly not a case where a player starts with zero. You end up at [506,128,128] and you cannot get to [506,0,256] because the rules of the game state that if two players with equal amounts of money are matched up, then the game ends. A player CANNOT end up with 0 dollars because they would have lost to someone with the same amount of money as them which ends the game. I don't know how else to say this.