Working out table plan possabilities with people not sitting near eachother

[DanM0611]

Hi all.
Having a small issue.
Trying to work out how to organise a table where some people cannot sit near others.
Here is the issue.

O won't sit next to G, K or J1
J2 won't sit next to J1
K won't sit next to J1 or O
G won't sit next to O
L won't sit next to P or J1

I won't sit next to anyone other than S, D, P or L

C is fine with any
G is fine with any

L must by O
D must by S
C must by J2

Try and keep J away from D

Attached below is the plan so far.

Hope this makes sense and someone can help fairly quick. Please move to correct section if needed.

Cheers, D - Dan

 

[Dr.Peterson]

Hi all.
Having a small issue.
Trying to work out how to organise a table where some people cannot sit near others.
Here is the issue.

O won't sit next to G, K or J1
J2 won't sit next to J1
K won't sit next to J1 or O
G won't sit next to O
L won't sit next to P or J1

I won't sit next to anyone other than S, D, P or L

C is fine with any
G is fine with any

L must by O
D must by S
C must by J2

Try and keep J away from D

Attached below is the plan so far.

Hope this makes sense and someone can help fairly quick. Please move to correct section if needed.

Cheers, D - Dan

Are you looking for one solution, or to count the number of ways (as implied by your title)?

Is there a reason there are two J's but your picture doesn't distinguish them? And which J is meant in "Try and keep J away from D"?

I take it your answer is wrong because of P and L, and J1 and K, being together. Perhaps you can tell us your strategy that led to this failure, and why you stopped there.

And can you tell us the context -- is this a real-life problem, or a puzzle you were given?

 

[blamocur]

Hi all.
Having a small issue.
Trying to work out how to organise a table where some people cannot sit near others.
Here is the issue.

O won't sit next to G, K or J1
J2 won't sit next to J1
K won't sit next to J1 or O
G won't sit next to O
L won't sit next to P or J1

I won't sit next to anyone other than S, D, P or L

C is fine with any
G is fine with any

L must by O
D must by S
C must by J2

Try and keep J away from D

Attached below is the plan so far.

Hope this makes sense and someone can help fairly quick. Please move to correct section if needed.

Cheers, D - Dan

Looks like a path in a graph problem.

 

[blamocur]

Try and keep J away from D

How many "J"s are there? I've counted 3: J, J1,J2.

 

[DanM0611]

Apologies all I appear to have made this more confusing that it needs to be.
Heres a better explination.

This is a real life situation where we need to work out who can sit by who at a dinner that will be held soon. I will now include all the names correctly so you can see properly.
I am looking for the best possible solution.


Ollie won't sit next to Georgia, Kirstey or Jess
Jack won't sit next to Jess
Kirstey won't sit next to Jess or Ollie
Georgia won't sit next to Ollie
Lorna won't sit next to Paula or Jess
Dan won't sit next to Jess (This is what makes it not possible)

Iona won't sit next to anyone other than Shona, Dan, Paula or Lorna

Chloe is fine with anyone
Georgia is fine with anyone

Lorna by Ollie
Dan by Shona
Chloe by Jack

Attached below is the best we could come up with right now.

 

[Dr.Peterson]

Starting with your suggestion, marking up their requirements, and moving people around to make corrections, I came up with this:

S - D - I - P - K - L - O - Ja - C - Je - G​

Does that work?

Someone else may well come up with a program to search the adjacency graph.

 

[Cubist]

Someone else may well come up with a program to search the adjacency graph.

I wrote such a program and it finds 178 possible solutions (ignoring clockwise/ anti-clockwise duplicates)

Therefore, @DanM0611, if you have any extra constraints for your guests then it might be possible to satisfy those too.

 

[The Highlander]

The 'best' solution to your 'problem' (and certainly the approach I would adopt in your circumstances) is to dispense with any place settings or a table plan altogether!
Just tell everyone that you have booked a (round?) table (for 10?) and they can sit anywhere they like on arrival ("first come, first served" will prompt 'em to turn up early if they want the seat, or neighbour, of their choice) and let them decide for themselves whom they wish to sit next to!
If the later entrants can't find a 'position' that suits them then they can take what's left and like it or lump it; they don't have to stay if they really don't want to. ?‍
It sounds like you're trying to cater for a bunch of real prima donnas; pandering to their petty insecurities can\only make them worse!
Doubtless, even if you could fit every one of them next to someone "acceptable" to them, these people would fall out with that individual before the dinner was over and then it really would be impossible to hold another event. ?

 

[Cubist]

The 'best' solution to your 'problem' (and certainly the approach I would adopt in your circumstances) is to dispense with any place settings or a table plan altogether!...

And how long did you work for the Diplomatic service?

 

[DanM0611]

Thanks everyone for your responses. This has turned quite entertaining. Its going to be a mixture of what the misses says... Theyre never wrong apparently. And what @The Highlander has suggested. ??

Cheers all