## Game Theory

What is the basis for reason? And mathematics?

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Arising_uk
Posts: 11151
Joined: Wed Oct 17, 2007 2:31 am

### Re: Game Theory

All I can think is that they say nothing and the mad king dies in five days time and that the number of cities is 10 or 13.
p.s.
Ah!
It must be something to do with the five days and the other or me not guessing and killing us and what not guessing implies?

So just pick a random number and work through or start from one of them seeing one city?

TSBU
Posts: 825
Joined: Wed Sep 14, 2016 5:46 pm

### Re: Game Theory

Arising_uk wrote:All I can think is that they say nothing and the mad king dies in five days time and that the number of cities is 10 or 13.
p.s.
Ah!
It must be something to do with the five days and the other or me not guessing and killing us and what not guessing implies?

So just pick a random number and work through or start from one of them seeing one city?
How many cities?
Anyway, if you and terrain were prisoners, you would be death XD. Surrender if you want and I'll tell you the answer.

vegetariantaxidermy
Posts: 6927
Joined: Thu Aug 09, 2012 6:45 am
Location: Narniabiznus

### Re: Game Theory

TSBU wrote:
Arising_uk wrote:All I can think is that they say nothing and the mad king dies in five days time and that the number of cities is 10 or 13.
p.s.
Ah!
It must be something to do with the five days and the other or me not guessing and killing us and what not guessing implies?

So just pick a random number and work through or start from one of them seeing one city?
How many cities?
Anyway, if you and terrain were prisoners, you would be death XD. Surrender if you want and I'll tell you the answer.
Is it a rotating tower?

vegetariantaxidermy
Posts: 6927
Joined: Thu Aug 09, 2012 6:45 am
Location: Narniabiznus

### Re: Game Theory

TSBU wrote:If one of them give a proper answer, they are both released, if one of them fail, both of them are killed. Maybe thats something that shouldbe said.

There is enough information, the king is not lying, and there are no tricks, they cant comunicate etc.

Of course, they can stay in their cells forever if they never answer.
Well you contradicted yourself. You said at first that only one had to be right. Then you said they would both die if one got it wrong i.e. they both had to get it right.

Arising_uk
Posts: 11151
Joined: Wed Oct 17, 2007 2:31 am

### Re: Game Theory

Okay, don't have an answer yet but my thinking has started like this -

A - I'm A, left column is what I could see if there are 13 cities, right is what would be seen otherside.
...........D1.......D2.......D3.......D4.......D5.......D6
0 13 -- Out
1 12 -- Out
2 11 -- Out
3 10 ------------------------Out
4 09
5 08
6 07
7 06
8 05
9 04
10 03 ------------------------Out
11 02 -- Out
12 01 -- Out
13 00 -- Out

A - I'm A, left column is what I could see if there are 10 cities, right is what would be seen otherside.
...........D1.......D2.......D3.......D4.......D5.......D6
0 10 -------------Out
1 09
2 08
3 07
4 06
5 05
6 04
7 03
8 02
9 01
10 00---------------Out

brb
Last edited by Arising_uk on Mon Oct 24, 2016 11:20 pm, edited 3 times in total.

vegetariantaxidermy
Posts: 6927
Joined: Thu Aug 09, 2012 6:45 am
Location: Narniabiznus

### Re: Game Theory

Arising_uk wrote:Okay, don't have an answer yet but thinking starts like this -

A - I'm A, left column is what I could see if there are 13 cities, right is what would be seen otherside.
...........D1.......D2.......D3.......D4.......D5.......D6
0 13 -- Out
1 12 -- Out
2 11 -- Out
3 10
4 09
5 08
6 07
7 06
8 05
9 04
10 03
11 02 -- Out
12 01 -- Out
13 00 -- Out

A - I'm A, left column is what I could see if there are 10 cities, right is what would be seen otherside.
...........D1.......D2.......D3.......D4.......D5.......D6
0 10
1 09
2 08
3 07
4 06
5 05
6 04
7 03
8 02
9 01
10 00

brb
I see you've given this some thought.

TSBU
Posts: 825
Joined: Wed Sep 14, 2016 5:46 pm

### Re: Game Theory

Your aproach is not bad, you are close to it. how many cities are there then?
You can even tell how many cities have seen the one in the east and the one in the west.

Terrapin Station
Posts: 1488
Joined: Wed Aug 03, 2016 7:18 pm
Location: NYC Man

### Re: Game Theory

TSBU wrote:If one of them give a proper answer, they are both released, if one of them fail, both of them are killed. Maybe thats something that shouldbe said.
If that's the case, then necessarily, they're either released or killed on the first query.

That's because on the first query, either at least one gives a correct answer, or they both give incorrect answers, right?

Well, if at least one gives a correct answer, then they're released.

If they both give incorrect answered, they're killed.

So on the first query, either they're released or killed. There's not an option for them to stick around to try again.

------------------------------------

I just realized that you weren't saying that they were queried and had to give an answer every day. But then there's not enough information that "five days" wouldn't be arbitrary.

Metazoan
Posts: 97
Joined: Sat Nov 10, 2007 11:23 am

### Re: Game Theory

Hi,

I got 13.

A split of 9 and 4

The preson seeing 9 would call at day 5.

I could be wrong and an off by one error is fatal in this game.

No more please, I am so far behind in my work and these don't help.

M

Terrapin Station
Posts: 1488
Joined: Wed Aug 03, 2016 7:18 pm
Location: NYC Man

### Re: Game Theory

Metazoan wrote:A split of 9 and 4

The preson seeing 9 would call at day 5.
Why would the split be 9 and 4 and why would the person seeing 9 "call at day 5"?

TSBU
Posts: 825
Joined: Wed Sep 14, 2016 5:46 pm

### Re: Game Theory

Metazoan wrote:Hi,

I got 13.

A split of 9 and 4

The preson seeing 9 would call at day 5.

I could be wrong and an off by one error is fatal in this game.

No more please, I am so far behind in my work and these don't help.

M

The answer is in small size, you are wrong

It is wrong, there are 13 cities, but they see 7 and 6 XD. C'mon if you are at work you have paper don't you? XD

First of all you get all the posible answers
First day.
0+13 X
1+12 X
2+11 X
3+10
4+9
5+8
6+7
or
0+10
1+9
2+8
3+7
4+6
5+5
The first day, if one of them see 13,12 0r 11 cities, then he knows the answer, so, the second day, if some of them see 0,1,or 2 cities, he knows that there aren't 13 cities, or the answer would have been said, so, if some of them is seeing 0,1, or 2 cities, the answer is 10.
second day
3+10
4+9
5+8
6+7
or
0+10 X
1+9 X
2+8 X
3+7
4+6
5+5
The process is simlar all the time, numbers are repeated just one time, now, if one of them is seeing 10,9 or 8 cities, he knows the answer.
third day.
3+10 X
4+9 X
5+8 X
6+7
or
3+7
4+6
5+5
fourth day if you are seeing 3,4,or 5...
6+7
or
3+7 X
4+6 X
5+5 X
fifth day
6+7

Terrapin Station
Posts: 1488
Joined: Wed Aug 03, 2016 7:18 pm
Location: NYC Man

### Re: Game Theory

So the important information missing from the set-up that should be made explicit is this:

* Every day, the jailer goes to them with one opportunity, and one opportunity ONLY, to answer.
* The prisoners are not required to answer. They must either answer or decline to provide an answer when asked the one time they're asked each day.
* When they choose to answer, they're only released if one gives the right answer, otherwise they're killed.
* Necessarily on the fifth day, they're able to answer correctly and be releaed.

Also, this still hinges on assuming that people are ideal rational agents, but they're not.

Metazoan
Posts: 97
Joined: Sat Nov 10, 2007 11:23 am

### Re: Game Theory

Hi,

For this to be an honest puzzle there would have to be exactly one solution.

Looking at the way I have done it I am missing why it is not a viable solution.

If one person does it as you did it and one as I did it then things may get out of sync.

The problem appears to be the possibility of simplifying mine by taking the steps on day 6 in day 4 etc.

Both solutions will come up with the correct answer but on different days.

Do you see a flaw in what I have done?

6 & 7 would come up on day 9 in my script.

Thanks,

M

Highlight the space below with your mouse to see my ramblings.
If you are not using the default colour scheme then close you eyes now.

Day
1 Only called as 13 if person sees 11,12,13
2 If you see 0 then call 10 The other person is seeing 10, The only others would be 11,12&13 which would have been called above.
3 If you see 10 then call 13 The other person is seeing 3, if they saw 0 then they would have called at 2
4 If you see 1 then call 10 The other person is seeing 9, if they saw 12 they would have called at 1
5 If you see 9 then call 13 The other person is seeing 4, if they saw 1 they would have called at 4
6 If you see 2 then call 10 The other person is seeing 8, if they saw 11 they would have called at 1
7 If you see 8 then call 13 The other person is seeing 5, if they saw 2 they would have called at 6
8 If you see 3 then call 10 The other person is seeing 7, if they saw 10 they would have called at 3
9 If you see 7 then call 13 The other person is seeing 6, if they saw 3 they would have called at 8
10 If you see 4 then call 10 The other person is seeing 6, if they saw 9 they would have called at 5
11 If you see 6 then call 13 The other person is seeing 7, if they saw 4 they would have called at 10
12 If you see 5 then call 10 The other person is seeing 5, if they saw 8 they would have called at 7

Arising_uk
Posts: 11151
Joined: Wed Oct 17, 2007 2:31 am

### Re: Game Theory

Cheers folks for trying not to spoil it for me

Slow is not the word for my thinking.

TSBU
Posts: 825
Joined: Wed Sep 14, 2016 5:46 pm

### Re: Game Theory

Terrapin Station wrote:So the important information missing from the set-up that should be made explicit is this:

* Every day, the jailer goes to them with one opportunity, and one opportunity ONLY, to answer.
* The prisoners are not required to answer. They must either answer or decline to provide an answer when asked the one time they're asked each day.
* When they choose to answer, they're only released if one gives the right answer, otherwise they're killed.
* Necessarily on the fifth day, they're able to answer correctly and be releaed.

Also, this still hinges on assuming that people are ideal rational agents, but they're not.
I've made it explicit. I said that they can stay there for ever if they never answer. I also said that they are both released as soon as one of them give a correct answer. I didn't say the fourth point, I said they were intelligent.

You just didn't get the answer, in a fair game, we can't always be perfect.

I'll send you a pm metazoan.

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