Queen: "They don't have bread? Why don't they eat cakes?" Attributed to Marie Antoinette, but, traced back to Rousseau. Well, I'm not a historician. And as always, thanks for the video. P.
best way? ask my mother to make the cuts. I still wonder how she manages to make them so perfect. as far as I know, never has anybody complained about it.
When I was studying Mathematics at Adelaide in the 1960s, this problem was posed in a paper for our Measure Theory course. After all, this problem is about the gastronomic value measure each of the eaters apply to different parts of the cake. A cutter, who may be one of the eaters, makes a radial cut in the cake and poises the knife over slowly rotating it, keeping the point in the centre, so sweeping out a sector of cake. The scrupulously honest eaters continuously integrate their measure of the value of the sector and call out when it reaches their fair share, i.e., 1/nth of the cake. The first to call out obviously values the piece more than the others, so there should be enough for the others to get at least their fair share. The cut is made, and the piece handed over, and the process is repeated to satisfy the desires of the remaining eaters.
This is logically equivalent to (and physically less messy than) the solution in my comment, which I also remember from the 1960s (no later than 1966). Jade, your history does not go back far enough!
@@johnbonnett5746: My reply was later than your comment by about a day; it looks like you noticed it as soon as was reasonable and there's nothing to be sorry about. I'm glad our memories line up on the general nature of the proof and the approximate time period. If only we could find some actual documentation to cite from that period -- but probably neither of us had any reason to preserve bibliographical notes on the subject.
So it only works if people are honest. So maybe at a birthday party where all people are friends, but definitely not when dividing resources as claimed in the video.
@@McFrax we're talking about very small numbers here. For n=2 already, lower bound is 4 but 2^2^2^2^2 already is a number with 19729 digits. I think you can see, that upper bound=2^(number with 19729 digits) is gonna be very large compared to 4. Also, upper bound grows much much faster... btw, the number of atoms in the known Universe has about 80 digits.
I am glad you mentioned about the metaphor thing. In one of the previous videos about a goat grazing half of the field, I made a joke about the engineer's approach and thousands of people seem to have taken it seriously and called mathematicians stupid 🤦♂️ Dear Mathematicians (And other scientists in general), as an engineer, I can not be more grateful for the foundation that you that you lay for us to build upon!
A cake is a metaphor for all the resources my mother has given me. And when she isn't looking, I take an extra slice, symbolizing my dissatisfaction with being fair.
Maybe instead of cutting the cake, we should cut one of the people. That reduces the number of people you need to cut cake for, therefore simplifying the problem.
I too, as a philosopher, take the problem seriously. I recommend the "Quit whining & enjoy what you get" philosophy & applying it to all cake people! 😂
This is so interesting and humorous for me, because I recently saw this diagram about how to cut cake in an equal way so that the cake (from a circle) equally can be distributed to how ever many people there are lol actually was really interesting imo. Basically it showed the cake being cut by circles, from the inside to out or whichever, then having those rows be individually cut to a specific size
you can remove the human factor. For example, you want to draw a blueprint for a new bedroom with bathroom and balcony in your house, but you have to decide three shapes to "cut" the floor on the second story, to strike a balance between the three areas. No ones being difficult there, and you want to make the best use of your hard earned money.
You explain things beautifully! It must be hard to explain this problem and find ways to summarize the assumptions (if the weight on the cake is continuous or not, if it depends on the participant, if cuts are restricted somehow, in which order participants cut and choose, if they can skip choosing, blah blah...) and not bore your audience. I would like to have the skill to do that graphically and just saying the bare minimum, as you do. A follow up on that "it's more complicated but it can be done in 5 cuts" would be nice.
I think you need to make a full length video about this. What are the limitations for the scenario? Does everyone value a different aspect of the cake or can they all value the same thing?
There was a neat algorithm described in Neil Stephenson's "Cryptonomicon" when Randy came up with a witty way to divvy up inheritance stuffs between lots of relatives
The mathematicians can keep arguing about how people are going to cut the cake, and who's going to get which pieces, while they argue I will be eating the whole thing.
Wow, what a simple recepe for 2-person case. Never occured to me before. I will suggest this now to my children next time they need to share something (fortunately, I only have two!)
Going off of the first model (one cuts, other chooses), I think we could build a working model for n persons. Example (where n=4) 1st person cuts the cake. 2nd person chooses for 3rd person, 3rd for 4th, etc. All parties are inclined to choose optimal slices so that they themselves will be similarly looked after. The cutter gets the last slice, and so will have been motivated to create slices with as fair a distribution of icing, toppings (etc.) as possible. The x factor is, as Up and Atom says, that people might value different slices more or less. Ultimately, open communication must be employed. If you don't say, "I like my cake with a lot of icing," then people won't prioritize that for you. Therefore, these preferences should be voiced before the first cut. This gives the slicer (1st person) the opportunity to create slices that are optimal for each person.
You can cut the cake into multiple slices and then use generalisations of the Thue-Morse sequence to generate the choice ordering. This works great in practice, especially for sharing things that are weighted polynomially.
I read an article about this an embarrassingly long time ago in Scientific American. The article pointed out that the remainder section(s) in real life situations would almost always go for attorney fees!
I didn't see this comment until I'd written my own. Apparently both of us remember something from longer ago than the video allows, and both of us may have seen it in Scientific American (Martin Gardner's column?). We seem to be two witnesses to the existence of some article that goes back further than Jade (upandatom) is aware of.
Thanks for this... This question has haunted me since I was a young boy, so always refused to let anyone bake me a cake for my birthday. Finally, I can get my own birthday cake.
I know how to solve this problem. Invite a bunch of Mathematicians to a party and get a really nice cake. Ask the smartest Mathematician to cut the cake perfectly, watch them all argue, then steal the cake and leave.
Here's my solution. A make on cut in the middle. C Chooses which side C&D takes. A&B gets the other side. C cuts so it's 4 pieces. B Chooses on A&Bs side. D Chooses on C&Ds side. Not perfect, but it's only cake. ;)
You should include links to resources for people who want to read more about the topic because the short itself has very little information about the details behind it.
i remember hearing about a fair way to cut a cake. the first person indicates what cut they would make, then everyone in turn can either pass or suggest a smaller cut. once everyone passes, the person who suggested the smallest cut takes his piece and the rest restart. since the person getting the piece suggested the cut, they'll be happy with their piece, and everyone that passed think they'll be happier with their piece from the rest than they would have been with the removed piece. In your example, if someone just wants the strawberry, they can pass on any piece that doesn't have the strawberry. anyone that wants the most cake possible can pass on any piece that's smaller than 1/# people, as the rest of the cake will have a bigger share per person.
A diplomat could have solved this problem in a heartbeat. Former German chancellor Ludwig Erhard is quoted by saying: "A compromise is the art of dividing the cake so that each person thinks they got the biggest part." I was tasked this as a kid regularly. I was given a bag of assorted candy, and I needed to divide it three ways between my dad, baby sister and I. Inknew what candies they liked, so I was usually left with the set I planned on having. Same with portioning ice cream into bowls. I think this made me who I am currently. Or messed me up, or both. 😂
Really interesting channel in general :) But it would be great if you also referenced article/paper for people that want to learn more about subject you talk about. Shorts are doing good job in sparking that interest but there have to be some follow up to that.
My first time in college, I had to take "topics in math for liberal arts majors" (actual name of the class, AKA math for non math people). There was a whole unit on cutting cakes fairly, it got so silly. I honestly thought they were just giving us busy work, but after watching this video it makes a bit more sense. More understanding in a minute than in a semester.
Actually, there is a quite easy way to solve this. To divide a cake between 4 people, each of the 4 gets exactly one chance to act/react. - The 1st person cuts a piece of cake they consider a fair part. (If all remaining persons agree, that will be his / her piece of the cake). - WHenever one of the other says the piece is too big, he/ she should reduce it to a piece they consider fair. (If all remaining persons agree, that will be his / her piece of the cake). And at the end of the first round, the last person who had reduced the piece will get that piece - Which each of the 4 already agreed to be either a fair share, or less than a fair share. So that leaves some remaining cake, plus 3 people who have to divide it. So they can follow the same process, each of the 3 gets exactly one chance to act or react. ...
When I was a kid, my parents always made sure that kids got the pieces they wanted. For example, we had a rectangular sheet cake and a kid at my birthday party wanted this very specific piece right in the middle. So, my mom cut the piece right out from the center. She always said “What’s more important: a neatly cut cake or a happy kid?”
To split a piece of cake fairly among N people: 1. If there is only one person, they get the whole piece. 2. A random person is selected to be the cutter, who cuts the piece into N fair slices (one per person). N-1 "tickets" are assigned to each slice. 3. Each non-cutter chooses their least favorite slice, then grabs one ticket for each other slice. The cutter gets all remaining tickets. 4. Repeat the whole process for each slice to split it fairly among its ticket-holders. Any person with multiple tickets acts multiple times at step 3 (once per ticket). --- Is that the algorithm? Should work, I think. I spent some time working it out now, but I probably heard the solution explained before, I think.
This is why you should never strive for perfect fairness. Always be willing to get slightly ripped off, since as long as you can be satisfied with your share of the cake, you will be able to settle disagreements with people much more often than if you never allowed yourself to be cheated out of anything.
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A mathematicians birthday party must be a very complicated affair.
Ha ha. Yes indeed :-)
That's why mathematicians should have at least 56 friends, so the probability of at least two people sharing the birthday is nearly 1.
Depends on the mathemetician. The most elegant solution in this circumstance is just have nearly no friends. xD
cuz 50% of the time, theyre sharing the bday with 100 other people :P
@@limitingchaosand then we can add the extra complexity of multiple cakes, with potential for flavor preference too
Just put the cake in a blender and give everyone an equally full glass of cake.
tf
No fair, mine was half empty but hers was half full
@@WyzrdCat You got the wrong address, the Philosophers' birthday party is next door
Drinkable cake (for consumption at the pink lake, with Sam Denby).
The cake's real mother will not agree to that
Oppenheimer tried to cut the cake down to the atomic level back in the 1940's. He realized it isn't a good idea.
"I am become death, destroyer of cake"
It was yellowcake
@@georgewang2947that is an Iranian specialty 😂
I thought Japanese loved it
@@anonymouscode1635the cake division ceremony was held there but they were not informed. I assume they don't like it
There is no fair way to divide a cake as no matter how it's divided, I want everything
*soviet anthem plays*
I guess fairness has different meanings for different people :D
@@Lattamonsteri There is no sich thing as fairness when it comes to sharing cake - or bacon
i guess we just need to buy the bakery instead
As above comment said , put it in a mixer/grinder
Give everyone glass of cake😂
Queen "Let them eat cake"
Masses: Well that's just not gonna cut it"
Queen: "They don't have bread? Why don't they eat cakes?" Attributed to Marie Antoinette, but, traced back to Rousseau. Well, I'm not a historician. And as always, thanks for the video. P.
Sounds like an Adrian Bliss Skit lmao
@@irfaanfarhat100% immediately imagined him saying it
Cut
@@NimsQuarlobut how do we get an envy free cut of the dictators head
best way?
ask my mother to make the cuts.
I still wonder how she manages to make them so perfect. as far as I know, never has anybody complained about it.
Well, what if nobody's complained and lived to tell the tale...
you had my attention at "imagine you have a cake"
Jade should have hearted this one, too.
Lmao every comment got hearted but yours😭😭
I tried this with my wife and she ate up the whole cake. Thank you Jane!
I'm going to need to buy quite a few cakes to really get to the bottom of this.
I have absolutely been the one to cut the cake and then still envy the piece the other person chose lol
Skill issues.
@@trucid2 human error, 100%
@@SteveJubsGrass is always greener… even when perfectly cut 🙃
@@J-sv9dp best reply
me every time coz i hope they don’t notice ones slightly bigger
Now, that's a "sweet" math problem, LoL 😂😂😂😂
I’m un-liking, only because I was 70th
@@jameswilkerson4412 LoL😂😂😂
Of course, now it has 163 ‘Likes’
@@jameswilkerson4412 yea😂😂
When I was studying Mathematics at Adelaide in the 1960s, this problem was posed in a paper for our Measure Theory course. After all, this problem is about the gastronomic value measure each of the eaters apply to different parts of the cake. A cutter, who may be one of the eaters, makes a radial cut in the cake and poises the knife over slowly rotating it, keeping the point in the centre, so sweeping out a sector of cake. The scrupulously honest eaters continuously integrate their measure of the value of the sector and call out when it reaches their fair share, i.e., 1/nth of the cake. The first to call out obviously values the piece more than the others, so there should be enough for the others to get at least their fair share. The cut is made, and the piece handed over, and the process is repeated to satisfy the desires of the remaining eaters.
This is logically equivalent to (and physically less messy than) the solution in my comment, which I also remember from the 1960s (no later than 1966). Jade, your history does not go back far enough!
@@larrykuenning5754 That sounds right to me. The last year of my formal mathematics was 1967. I'm sorry I did not notice your reply before.
@@johnbonnett5746: My reply was later than your comment by about a day; it looks like you noticed it as soon as was reasonable and there's nothing to be sorry about. I'm glad our memories line up on the general nature of the proof and the approximate time period. If only we could find some actual documentation to cite from that period -- but probably neither of us had any reason to preserve bibliographical notes on the subject.
now, apply that to warfare responsibilities amongst the U.N.
So it only works if people are honest. So maybe at a birthday party where all people are friends, but definitely not when dividing resources as claimed in the video.
I'm impressed that mathematicians have abstracted that problem in the first place, let alone solved it.
The best part is while the upper bound in n^n^n^n^n^n while the lower bound is just n^2
when mathematicians have skill issue
Frankly, n^2 is still a lot.
@@McFrax we're talking about very small numbers here. For n=2 already, lower bound is 4 but 2^2^2^2^2 already is a number with 19729 digits. I think you can see, that upper bound=2^(number with 19729 digits) is gonna be very large compared to 4. Also, upper bound grows much much faster...
btw, the number of atoms in the known Universe has about 80 digits.
"skill issue", he says! @@cubing7276
Wait didn't 3 people do if in 5 cuts or less than n^2 (9)
I am glad you mentioned about the metaphor thing.
In one of the previous videos about a goat grazing half of the field, I made a joke about the engineer's approach and thousands of people seem to have taken it seriously and called mathematicians stupid 🤦♂️
Dear Mathematicians (And other scientists in general), as an engineer, I can not be more grateful for the foundation that you that you lay for us to build upon!
If you are at a mathematical festival, always choose the first toilet. No-one else will.
Ye Olde' Secretary Outhouse Problem
"Mathematician festival" makes them sound like they have an entire culture lol
A cake is a metaphor for all the resources my mother has given me. And when she isn't looking, I take an extra slice, symbolizing my dissatisfaction with being fair.
This is why cupcakes are awesome. Everyone just picks one and the leftovers go home with the birthday child.
Maybe instead of cutting the cake, we should cut one of the people. That reduces the number of people you need to cut cake for, therefore simplifying the problem.
But then you have the problem of dividing the person among the others.
That escalated quickly
There be zombies among us lol
Mathematically correct. Technically the best kind of correct.
That way I eat whole cake 😂
I love this channel bc you tell us problems that have been solved but nothing about the solution, not even the equation
I too, as a philosopher, take the problem seriously. I recommend the "Quit whining & enjoy what you get" philosophy & applying it to all cake people! 😂
But I want to have my cake and eat it too lol
This is so interesting and humorous for me, because I recently saw this diagram about how to cut cake in an equal way so that the cake (from a circle) equally can be distributed to how ever many people there are lol actually was really interesting imo.
Basically it showed the cake being cut by circles, from the inside to out or whichever, then having those rows be individually cut to a specific size
This sounds like less of a maths problem and more like humans being difficult.
you can remove the human factor. For example, you want to draw a blueprint for a new bedroom with bathroom and balcony in your house, but you have to decide three shapes to "cut" the floor on the second story, to strike a balance between the three areas. No ones being difficult there, and you want to make the best use of your hard earned money.
You explain things beautifully! It must be hard to explain this problem and find ways to summarize the assumptions (if the weight on the cake is continuous or not, if it depends on the participant, if cuts are restricted somehow, in which order participants cut and choose, if they can skip choosing, blah blah...) and not bore your audience. I would like to have the skill to do that graphically and just saying the bare minimum, as you do.
A follow up on that "it's more complicated but it can be done in 5 cuts" would be nice.
Step 1: assume the cake is a sphere. 😂
Step 2 : And let the volume of of cake is infinite, problem solved
I love the simplicity of “one person cuts, the other chooses.” Immediate incentive for the cutter to make the cut as fair as possible.
The team of researchers still wasn't able to enjoy a meal together.
That was much clearer than the first short on the envy-free-cake-cutting. Great job!
I think you need to make a full length video about this. What are the limitations for the scenario? Does everyone value a different aspect of the cake or can they all value the same thing?
There is a good video from TH-cam channel Numberphile titled " Equally sharing a cake between 3 people'
My goodness... to be able to listen to you while eating your cake sounds like a dream 😜
Now I want cake :(
The cake is a lie.
And there is no spoon.
I am glad they solved it. Been sitting here with this cake for the past 40 years. I can finally move on to doing laundry.
Cutting it in atoms and divide it 😅
I kinda want to know how to cut the cake when there are 3 people
I recall a numberphile video on exactly that. I forget what it's called, but I'm sure you can find it!
I never realized cake cutting was a metaphor, I’ve always thought mathematicians were just interested in ways to cut cake
This is why on my birthdate party i always do total people / 3 of cakes...
The hard part is having knifes for all cakes.
There was a neat algorithm described in Neil Stephenson's "Cryptonomicon" when Randy came up with a witty way to divvy up inheritance stuffs between lots of relatives
It doesn't matter how accurately or fairly you cut the cake; someone will always complain
Aren’t we all just born whiners!
The mathematicians can keep arguing about how people are going to cut the cake, and who's going to get which pieces, while they argue I will be eating the whole thing.
Let's hope Graham's number of people don't want to share a big cake equally then.
Siblings will cut the cake in an infinite number of pieces to make it fair
"You'll get nothing and like it. Now who else wants to complain?" This solves the problem.
Parent: Here's your cake. If you don't want it, I will eat it for you.
Wow, what a simple recepe for 2-person case. Never occured to me before. I will suggest this now to my children next time they need to share something (fortunately, I only have two!)
Forget the cake , I just fell in love with her
Going off of the first model (one cuts, other chooses), I think we could build a working model for n persons.
Example (where n=4)
1st person cuts the cake.
2nd person chooses for 3rd person, 3rd for 4th, etc.
All parties are inclined to choose optimal slices so that they themselves will be similarly looked after. The cutter gets the last slice, and so will have been motivated to create slices with as fair a distribution of icing, toppings (etc.) as possible.
The x factor is, as Up and Atom says, that people might value different slices more or less.
Ultimately, open communication must be employed. If you don't say, "I like my cake with a lot of icing," then people won't prioritize that for you.
Therefore, these preferences should be voiced before the first cut. This gives the slicer (1st person) the opportunity to create slices that are optimal for each person.
That’s why the best outcome is achieved by mutual compromise.
I have pondered this problem for many years. Thank you for talking about it!
One of the nicest math books I've ever read was called precisely that "How to cut a cake (and other mathematical conundrums)" 😄
Love your videos. Momentarily I am back at university. Thank you.
when people are jobless enough to write such complex pieces of code
Hey I think this re-upload is much clearer in explaining the concept.. Thank you for introducing a new concept for me...👌
You can cut the cake into multiple slices and then use generalisations of the Thue-Morse sequence to generate the choice ordering. This works great in practice, especially for sharing things that are weighted polynomially.
The best mathematical principle is to choose the winner by rock, scissors, and paper.
Thanks for teaching us maths in an easy to understand way ❤❤
Ah yes, the cake smoothie. Perfectly devided and distributed.
I read an article about this an embarrassingly long time ago in Scientific American. The article pointed out that the remainder section(s) in real life situations would almost always go for attorney fees!
I didn't see this comment until I'd written my own. Apparently both of us remember something from longer ago than the video allows, and both of us may have seen it in Scientific American (Martin Gardner's column?). We seem to be two witnesses to the existence of some article that goes back further than Jade (upandatom) is aware of.
You know, you could just... not share the cake. That's an option.
Thanks for this... This question has haunted me since I was a young boy, so always refused to let anyone bake me a cake for my birthday. Finally, I can get my own birthday cake.
I know how to solve this problem. Invite a bunch of Mathematicians to a party and get a really nice cake. Ask the smartest Mathematician to cut the cake perfectly, watch them all argue, then steal the cake and leave.
There are even more "cake-cutting" variants out there, such as people not knowing what they prefer or actively being deceptive about what they prefer.
One moral of the lesson: Just bring plain cakes with no decorations on it to a gathering of mathematicians.
It's always the computer scientists.
I ain’t here for information. You just that pretty😭😤
I love the little hair flick at the start of every video lol
Brilliant discussion! 👍🏽♥️
Ah yes, math and its importance displayed in full power
Here's my solution.
A make on cut in the middle.
C Chooses which side C&D takes.
A&B gets the other side.
C cuts so it's 4 pieces.
B Chooses on A&Bs side.
D Chooses on C&Ds side.
Not perfect, but it's only cake. ;)
Wait they solved it for 4+ people?? I've been under a rock!!
You should include links to resources for people who want to read more about the topic because the short itself has very little information about the details behind it.
This.
i remember hearing about a fair way to cut a cake. the first person indicates what cut they would make, then everyone in turn can either pass or suggest a smaller cut. once everyone passes, the person who suggested the smallest cut takes his piece and the rest restart. since the person getting the piece suggested the cut, they'll be happy with their piece, and everyone that passed think they'll be happier with their piece from the rest than they would have been with the removed piece. In your example, if someone just wants the strawberry, they can pass on any piece that doesn't have the strawberry. anyone that wants the most cake possible can pass on any piece that's smaller than 1/# people, as the rest of the cake will have a bigger share per person.
The only thing about the two person cutting of the cake is that the two people tend to argue on who will cut and who will choose
The ham sandwich theorem sounds like a better solution to this. Just add more cuts (and more spatial dimensions) for each person
A diplomat could have solved this problem in a heartbeat. Former German chancellor Ludwig Erhard is quoted by saying: "A compromise is the art of dividing the cake so that each person thinks they got the biggest part."
I was tasked this as a kid regularly. I was given a bag of assorted candy, and I needed to divide it three ways between my dad, baby sister and I. Inknew what candies they liked, so I was usually left with the set I planned on having. Same with portioning ice cream into bowls. I think this made me who I am currently. Or messed me up, or both. 😂
Really interesting channel in general :) But it would be great if you also referenced article/paper for people that want to learn more about subject you talk about. Shorts are doing good job in sparking that interest but there have to be some follow up to that.
My first time in college, I had to take "topics in math for liberal arts majors" (actual name of the class, AKA math for non math people). There was a whole unit on cutting cakes fairly, it got so silly. I honestly thought they were just giving us busy work, but after watching this video it makes a bit more sense. More understanding in a minute than in a semester.
If I had a teacher like you, I would be very distracted. 😚😘😘
I, for one, remember the Numberphile Cake Video Incident.
"Imagine you have a cake..."
Hold that thought, I'm making a quick run to the bakery.
That rapid head turn as the video begins… have you been taking lessons from Vsauce?
Instructions unclear. Now I have a smoothie
"for two people, it's a cakewalk"
😂
I eat entire cakes alone sometimes.😂
so that's why mathematicians have only three people in birthday parties.
Schrödinger’s cake: You can have your cake and eat it, too.
Cheers, Jade! 😘🤓🥰
Me buying a cake with just frosting 💀💀
The accountants are getting their slice first and leaving us with the crumbs
three mathematicians are having a party and a fourth walks in…
Actually, there is a quite easy way to solve this.
To divide a cake between 4 people, each of the 4 gets exactly one chance to act/react.
- The 1st person cuts a piece of cake they consider a fair part. (If all remaining persons agree, that will be his / her piece of the cake).
- WHenever one of the other says the piece is too big, he/ she should reduce it to a piece they consider fair. (If all remaining persons agree, that will be his / her piece of the cake).
And at the end of the first round, the last person who had reduced the piece will get that piece - Which each of the 4 already agreed to be either a fair share, or less than a fair share.
So that leaves some remaining cake, plus 3 people who have to divide it.
So they can follow the same process, each of the 3 gets exactly one chance to act or react.
...
one of my favorite things about mathematicians is how they will come up with the most unhinged way to cut something and it's always so much fun
When I was a kid, my parents always made sure that kids got the pieces they wanted. For example, we had a rectangular sheet cake and a kid at my birthday party wanted this very specific piece right in the middle. So, my mom cut the piece right out from the center. She always said “What’s more important: a neatly cut cake or a happy kid?”
my mom would say the neatly cut cake
RNG fixes everything.
To split a piece of cake fairly among N people:
1. If there is only one person, they get the whole piece.
2. A random person is selected to be the cutter, who cuts the piece into N fair slices (one per person). N-1 "tickets" are assigned to each slice.
3. Each non-cutter chooses their least favorite slice, then grabs one ticket for each other slice. The cutter gets all remaining tickets.
4. Repeat the whole process for each slice to split it fairly among its ticket-holders. Any person with multiple tickets acts multiple times at step 3 (once per ticket).
---
Is that the algorithm? Should work, I think. I spent some time working it out now, but I probably heard the solution explained before, I think.
Could be done with at most (N - 1)! cuts.
Call me when mathematicians discover how to have your cake eat it too.
"Why do u want her slice?? theyre all mathematically calculated and perfectly cut"
"I want 2"
Thing is, everyone will still be envious because everyone always want more cake.
This is why you should never strive for perfect fairness. Always be willing to get slightly ripped off, since as long as you can be satisfied with your share of the cake, you will be able to settle disagreements with people much more often than if you never allowed yourself to be cheated out of anything.
You're telling me that for forty years I've been cutting my cake wrong?