Equally sharing a cake between three people - Numberphile

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This video features Dr Hannah Fry.
Her book mentioned is "The Mathematics of Love".

A clarifying note from Hannah: n^n^n^n^n^n is the maximum number of cuts in the n person case.

Something we could have made clearer... Bob's trimmed piece still carries the status of his "first choice", so if Charlie leaves it, Bob will (must) pick it... otherwise he'll pick the one that was his original "second choice"... The upshot of this is that there's no chance Alice will be left with the trimmed piece after everyone takes their first piece. And Bob remains envy free under these conditions too.

Editing and animation in this video by Pete McPartlan

We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science.

NUMBERPHILE

Videos by Brady Haran

[shubhankarpathak]

I used this and everyone left...I got the whole cake !!thank you❤️

[decoder]

Plot twist: with all that cutting, you lose 1/3 of the cake in the crumbs that fall out

[ojaimark]

My favorite part about this is that it doesn't seem like it but it could actually be practical for settling children's siblings disputes. Not because the kids will appreciate the fairness and mathematical/logical beauty, but because they'll get so fed up with the long process they'll be more than happy to drop the squabble and just take a piece of cake.

[BlobVanDam]

This is why you never invite a mathematician to a birthday party.

[greendogg]

Lesson learned, never share a cake with more than one mathematician, it'll take far too long

[WannaComment]

I prefer the classic method:
- cut however
- argue over who deserves the big piece
- spew childish insults
- engage in mortal combat
- winner takes it all

[Nacho-djzm]

that is the saddest cake i've ever seen

[limetimemusic]

So this is what people who write exam questions spend their time doing

[jimmykeffer]

Moral: never share cake with a mathematician

[numberphile]

Something we could have made clearer... Bob's trimmed piece still carries the status of his "first choice", so if Charlie leaves it, Bob will pick it... otherwise he'll pick the one that was his original "second choice"... The upshot of this is that there's no chance Alice will be left with the trimmed piece after everyone takes their first piece.

[GiskardRevenlov]

This has to be one of the most confusing and convoluted way to cut a cake

[arn]

Let's use the dryest, shittest most crumbly cake in a cake cutting experiment shall we?

[deldia]

Steal a Mercedes badge and thrust it into the top of the cake

[liverturcxdanpavs]

After making so many cuts, most of the cake remains crumbled on the plate

[AbdulHaseeb-zepu]

my loved ones: please abdul we want to eat the cake it's been an hour.
me on my birthday: so now you cut the trimmings-

[__teles__]

It's not equal sharing, its poltical bargaining meaning everyone feels cheated but can't complain about it.

[spaceddoggo]

Split it into 4, split the last 4 into 4, split the last 4 into 4, keep doing it and you'll have infinite food. World hunger solved.

[moara]

Easy solution: buy more cake.

More cake is always the right answer

[SgtAbramovich]

Different trios of professionals splitting a round cake:
*Mathematicians*
See above

*Physicists*
Search for the cake's fundamental frequency, make a sound exactly three times that frequency and cut it precisely at the nodes.

*Engineers*
Divide by three? Three is like so close to five, isn't it? And five is so close to ten, might as well cut it roughly in ten pieces, give each one three and give the remaining slice to the heftier one.

*Philosophers*
But really, what is a cake?

*Lawyers*
Discuss why you should get the whole cake instead, because you deserve it and others wanting it is a violation of your rights.

*Chemists*
Any way of dividing the cake fairly would be integrally destructive.

*Bankers*
What cake?

[kingpopaul]

Why cut the cake when you can just grind it and divide it by weight?