Cooking rota

[wildeabandon]

Say you have three people, and sometimes they all eat together, and sometimes they eat together in each of the pairs. Say you want to keep track of whose turn it is to cook in each of these three configurations. Say you'd quite like some kind of physical method of doing this so it can be incremented in the kitchen. I'm thinking it must be possible with jars and beads, or some kind of abacus like thing, but I can't entirely pinpoint how best to do it. If it's something that it's easy to make a second copy of for keeping track of whose turn it is to buy dinner in the same groupings that would be awesome.

Any ideas?

Comments

[robert_jones]

It seems to me that we don't want four separate rotas, one for the three of us and one for each of three pairs.

Let's say between the three of us, cooking has gone C, J, S

Then S isn't here, and it's your turn to cook. When next we three eat together, it will be my turn to cook, then yours, then Ramesh's.

If you, like it will go C, J, S, [C], J, C, S and not C, J, S, [C], C, J, S, which would be silly. Similarly if we had several turn of pairwise cooking, then we would fit pairwise into the three-way rota however was appropriate, e.g. C, J, S, [C], [J], C, J, [C], S, J, C, etc.

[robert_jones]

So I think you could do it with a triangle, with C, J and S on the three sides. Then we rotate the triangle by 120° for three-way cooking and reflect it along the appropriate axis for two-way cooking.

[ciphergoth]

Every time you cook a meal, move a bean from every jar for a person you cooked for into your jar.

[wildeabandon]

So it's always the turn of the person with fewest beans in their jar to cook? Yes, that sounds sensible. I think it would give slightly too much value the additional difficulty in cooking for an extra person, except Ramesh being veggie means that it often is twice as difficult.

Thanks.

[wildeabandon]

That's equivalent to the three jars suggested below, isn't it? So now we just have to decide which is easier to implement.

[meihua]

This is beautifully simple. Thank you.

[robert_jones]

No, it's not equivalent. Taking x, y, z to mean C has x beans, J has y and S has z, and allowing alphabetical order to break ties, the sequence C, J, S, [C], [J], C, J, [C], S, J would go

3, 3, 3
5, 2, 2
4, 4, 1
3, 3, 3
4, 2, 3
3, 3, 3
5, 2, 2
4, 4, 1
5, 3, 1
4, 2, 3
3, 4, 2

Which would make it S's turn to cook, when it should be yours.

[robert_jones]

Or more simply, the sequence, C, [J] goes

3, 3, 3
5, 2, 2
4, 3, 2

So as between you and me, I have to cook twice in a row!

[robert_jones]

It doesn't matter how beautifully simple it is, when it gives the wrong answer!

[robert_jones]

Also, how can you call a solution involving three jars and at least six beads simpler than one involving one triangle?

[meihua]

I saw who posted it and assumed it was correct. I'll look forward to seeing the discussion.

[meihua]

Because the triangle solution as described didn't make any sense to me, and also because it doesn't seem to handle the situation where it just so happens that someone cooks a few times in a row, just because that's how it works out.

[wildeabandon]

Does it give the wrong answer to the question as I stated it? (I agree that your solution is a better one for the question as I should have stated it)

[andrewducker]

I'd ignore the configurations, as otherwise you end up in situations where someone would have to cook twice in succession (which doesn't seem fair) - and it's not much harder to cook for three than for two.

In which case a simple "Take it in turns to cook, and if you missed your turn then it's your turn next" rule would probably work best, and be fair 95% of the time.

[robert_jones]

If X cooks when it's Y's turn to cook, that's a private arrangement between X and Y which doesn't affect the rota (in particular, it ought not to affect the position of the third person).

[robert_jones]

Ok, wrong is too strong, but it suffers from the flaws pointed out by andrewducker below.

[robert_jones]

The problem is, this would work well if the three people all lived together. In fact (although Sebastian didn't say so), one of them is only there 30% of the time, or so. It doesn't seem fair to treat him as 'missing his turn' on the large number of occasions when he isn't here!

[robert_jones]

Because the triangle solution as described didn't make any sense to me

It's really pretty straightforward. The state of the system at any time is an ordered triad of {C, J, S}. The person in the lowest numbered position cooks. For three-way cooking the triad cycles, for two way cooking, those two elements swap.

Admittedly you would end up with me cooking twice in a row if the position is (J, C, S) and I eat once with Sebastian (taking us to (C, J, S) and once with Ramesh (taking us to (C, S, J), but that's unavoidable, because both of Ramesh and I 'cooked last', and it doesn't come up very often.

[wildeabandon]

I'm not sure about this. I mean, I agree that it shouldn't affect the position of the third person, but giving a bead to Y rather than X won't affect their overall bean balance, and thus their position on the rota would work out in the end. And it would be quite useful to have something which does allow for flexibility.

[robert_jones]

Yes, but as we've already established if X and Y cook pairwise, that effects Z's position.

[robert_jones]

affects, obviously

[wildeabandon]

Yes, although as you say, the triangle thing also leads to people cooking twice in a row (I think that it's less rare than you think, because I swap between pairwise sets more often than you, but also enjoy cooking more), and it has the flexibility advantage. I think on balance I prefer the triangle though.

[andrewducker]

Being away 70% of the time would affect things a lot. It'd basically mean that he'd cook every time he was there, which would be unfair.

I suppose that what you actually want is to keep the ratio of "times cooked/"times eaten" the same between people.

Which basically means keeping track of both numbers (via a whiteboard and mental arithmetic). Or the beads method, which should be fine most of the time.

I do worry that any mechanical method will have intermittent problems - not least at times when The Method says it's your turn to cook, but real life makes it tricky.

[robert_jones]

not least at times when The Method says it's your turn to cook, but real life makes it tricky

That's a problem with having a rota, not with having a mechanical system for implementing it.

[andrewducker]

All rotas are mechanical systems :->