h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

In our family no-one would cut the cake. We'd just refuse. All of us. Damn thing would go stale. This may say more about us than it does about the cake problem.

What about weighing it, cutting a third/quarter/half and weighing that? There may be icing/sponge/jam ratio issues to be ironed out but we put a man on the moon didn't we?

Hi Balatro

Yes, I mentioned that you can weigh each slice - in the bit about impartial referees.

You raise a very good point about icing/sponge/jam ratio issues. I would have written about this more, but the entry was getting a bit long.

The thing is, many cakes are what a mathematician would call 'heterogeneous', ie they aren't the same all the way through (there might be cherries on the top or uneven filling for example).

This causes a problem as you say with exact weighing, and also with geometric cutting - some people might want the piece with the cherry on top.

Now, the four methods I cover should deal with most cases like this. You have the chance to shout "Cut!" when the slice is adequate for you, no matter what its size is, and you can always accept a smaller slice to get the cherry.

Does this make sense?

Icy

In my family, the cake wouldn't last long enough to get near a knife. This also says more about us than the cake problem.

Could you divide the cake into lots and lots of little pieces, all of a roughly average size, and then give each person a random selection, or is this classed as trimmings? I suppose this brings up additional problems of numbers of pieces, edge effects and caster sugar spillage.

Also, does the trustworthiness of any mathematical theorem depend on how fat the mathematician is?

I think you've hit the nail on the head, there! This is more of a philosophical problem than a mathematical one, and I was delighted to see that the Editors also filed this one under Philosophy.



Yes, that's one way, and I think it would help to share out the non-uniform features. So long as the pieces are no smaller than bite-sized.

Another way is if there are five people, say, then divide the cake into ten. Alice chooses piece 1 and piece 10, Bob chooses piece 2 and piece 9, Chris chooses piece 3 and piece 8, etc.

Icy