To greet multiple recipients in an email, follow these steps:
1. Choose a header format.
2. Write an appropriate salutation.
3. Double check accuracy.
4. Know your audience.
5. Use a group name that describes the recipient’s role or position.
6. List individual names.
7. Use a greeting.
8. Select a greeting that sets the tone for the message.
9. Choose the right greeting for the recipient.
10. Include all names, if possible.
In an office or school setting, use “Dear All” for general announcements. In a professional or formal setting, use formal salutations like “Dear Mr. Smith” or “Dear Professor Johnson.”
In a business letter, write the first person’s name, followed by their title at the company, and then the next person’s name, title, and so on.
In summary, addressing multiple recipients in an email requires knowing your audience, using a group name, selecting an appropriate greeting, and double checking accuracy. By following these guidelines, you can create a professional and respectful email that effectively addresses multiple recipients.
An effective email includes a concise subject line, a respectful greeting, an introduction, and proper email etiquette. To address multiple people in an email, include their names in the salutation and use the ‘To’ field to add multiple email addresses. Start by listing their names in the body of the email, followed by their titles. Personalize your salutation, show appreciation, reference something unique to the interviewer, reiterate qualifications, and state interest in the conclusion. Use a professional signature.
When addressing multiple people, include their names in the salutation. For larger groups, use a common salutation like “Dear Team.” For emails to a few people, use “Dear first name, first name.” For larger groups, use a more general greeting like “Dear Team.”
For professional or formal settings, use formal salutations like “Dear Team,” “Dear Colleagues,” or “Dear Team.” Include a cc: after the names of recipients to inform them of who else has received the letter. Remember to use individual or group names in the salutation and gender-neutral language in the email body.
📹 Equally sharing a cake between three people – Numberphile
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 …
How do I address an email to a group of people?
Group: Best in formal settings. Hi: More casual. Hey: Very casual. Use it when it’s appropriate. Hi folks is my favorite because it sounds friendly. Email is here to stay. It’s the fastest way to get your message to someone directly. It helps form a personal connection. At Boomerang, we’ve analyzed 300,000 emails to see which ones got responses. (See the full results here.) One thing was clear: Emails with a greeting were more likely to be answered than those without.
How do I address 3 people in a letter?
When writing to one, two, or three people, say their names in the salutation, e.g., Dear Tom, Mia, and Jim. Good afternoon, Jose and Camila.
Considerations: Even if you’re using proper email etiquette, don’t communicate electronically at the expense of personal interaction. People often need to discuss things face-to-face. There are times when no substitute will do. Whether you’re breaking up with your boyfriend or asking your boss for a raise, watch what you say and how you say it. The computer brings people together, but its impersonal nature can lead to remarks that people wouldn’t think of saying in person. Stay courteous. If you need to, tape a note to your computer. Be careful when you click “Send.” What you say online can’t be taken back. Once you hit “Send,” your message can be saved and forwarded by anyone. Words can hurt, destroy friendships, and ruin careers.
How to Address Multiple People in an Email When writing to one, two, or three people, include each person’s name in the salutation. Dear Tom, Mia, and Jim. Good afternoon, Jose and Camila.
How do I address four people in an email?
If you’re talking to more than four people, don’t use names. Use a general term like “team” or “everyone.” Mention the department name if you can. For example:
- Hello team
- Dear team
- Hi everyone
- Dear sales department
- Hello development team
If you know the group well, you can use a nickname. However, you must never be so formal in an academic or business setting. Even if you’re close with the people you’re emailing, the bosses may want employees to be professional at work. Also, don’t use gendered group terms. Group terms like “gentlemen,” “ladies,” or “guys” may not represent the group you’re emailing, so don’t use them. Most gendered group terms are not professional. Even “gentlemen” can sound out of place in most workplaces. If it’s not used around the office, don’t use it in the email.
How do you address an email to 4 recipients?
If you’re talking to more than four people, don’t use names. Use a general term like “team” or “everyone.” Mention the department name if you can. For example:
- Hello team
- Dear team
- Hi everyone
- Dear sales department
- Hello development team
If you know the group well, you can use a nickname. However, you must never be so formal in an academic or business setting. Even if you’re close with the people you’re emailing, the bosses may want employees to be professional at work. Also, don’t use gendered group terms. Group terms like “gentlemen,” “ladies,” or “guys” may not represent the group you’re emailing, so don’t use them. Most gendered group terms are not professional. Even “gentlemen” can sound out of place in most workplaces. If it’s not used around the office, don’t use it in the email.
How do you address a letter to 4 people?
In a business letter, write the person’s name, then a comma, then their title. Write the next person’s name, title, and so on on a new line. Include all names. If you’re sending the letter to one address, include all names. You may write a letter to multiple people. You may be sending a Christmas letter or wedding invitation to a large family. You may be sending a cover letter for a job with multiple hiring managers. You have different ways to address a letter to multiple people. Business letters have a header in the upper left-hand corner. This is a list of information about the company and the letter recipients. You still need to include the header in a business letter to multiple recipients. Write the recipient names in the top right corner. Write the names using formal titles (e.g., Dr. Nora Woods) and separate them by a comma. Then, write the name of the company on the next line and the company’s address. On the last line, write the city, state, and zip code.
How do you address 5 people in an email?
If you’re talking to more than four people, don’t use names. Use a general term like “team” or “everyone.” Mention the department name if you can. For example:
- Hello team
- Dear team
- Hi everyone
- Dear sales department
- Hello development team
If you know the group well, you can use a nickname. However, you must never be so formal in an academic or business setting. Even if you’re close with the people you’re emailing, the bosses may want employees to be professional at work. Also, don’t use gendered group terms. Group terms like “gentlemen,” “ladies,” or “guys” may not represent the group you’re emailing, so don’t use them. Most gendered group terms are not professional. Even “gentlemen” can sound out of place in most workplaces. If it’s not used in the office, don’t use it in the email.
How do I address multiple people in a letter?
A carbon copy is usually marked by the words cc or copies to, followed by a colon. Multiple recipients are listed using their full names. For example, cc: Dr. Mark Brook, Dr. Nora Woods. If the recipients are from a different business, add the business name in parentheses after the names. For example, cc: Dr. Mark Brooks (Penbrook Medical Associates), Dr. Nora Woods (Shepherd Medical Hospital).; The term “carbon copy” means copies of the letter will be sent. If you’re using a carbon copy, make sure everyone gets their own copy. Don’t use a carbon copy if you’re only sending the letter to one person. When sending a letter to multiple people, say who gets a copy by using cc for carbon copy. List each recipient on a separate line in the header with their name, title, and address. This lets everyone see who else is included.
You may send a business letter to an entire office or a very large group. You can use an informal word to address the letter in this case. If you’re sending a mass email to your entire company, you can write something like “Dear Associates” or “Dear Colleagues” if your company has over 10 people. It’s better to get a name.
Can you address 3 people in an email?
Use commas or semicolons to separate names, and end with a colon or comma before the body of the email. You could write “Dear John, Mary, and Sam,” “Hello Dr. Smith, Ms. Jones, Mr. Lee,” or “Hi Alice, Bob, Carol, and Dave.” Email is a common way to communicate with multiple people, but it can be tricky to find the right tone and wording for your greetings. How do you address multiple people in an email without sounding impersonal, rude, or confusing? Here are some tips for writing a professional email greeting.
Selected by the community. Learn more. Think about the goal of the email. If it’s a general update, a general greeting is best. This avoids extra work for readers. If you’re introducing a group, your greeting is important.
How do you write an email to multiple recipients?
Let’s start. Log in to Gmail. … Write your message. Time to write that email. … BCC. Gmail has three options next to the To field: CC and BCC. … Fill in the BCC fields. Enter the email addresses here. … Send. Ever sent an email to a lot of people without sharing their addresses?
Or maybe you want to personalize your message for each recipient without spending too much time? We often need to send emails to multiple people for different reasons, such as sales, marketing, recruitment, or membership activities. But doing this manually can be tedious and risky. There are smart solutions to help you send and track emails to multiple recipients separately.
How do you address a group of people?
To write a professional salutation for a group, use a generic term like “Dear Team,” “Hello Everyone,” or “Greetings.” This is a safe, neutral option for internal communications, casual messages, or general announcements. Avoid vague or casual terms like “To Whom It May Concern” or “Hey Guys” as they may sound impersonal or disrespectful. It’s good to use phrases like “Dear Valued Team,” “Dear Colleagues,” or “Dear Attendees” when communicating with a larger audience. For a department, phrases like “Dear Marketing Team” or “Dear Engineering Team” are suitable. “Dear Workshop Attendees” or “Dear Conference Participants” are examples of event-specific greetings.
How do I mention two people in an email?
Use both people’s names after your greeting, like “Hello Max and Ava,” or “Good afternoon, Mr. Johnson and Mrs. Smith.” Include both people’s email addresses in the “To” field if the message requires both of their attention. CC someone to include them in the message. Be clear in the email about what you need from each person. If you’re starting a formal email, use a simple greeting before writing out the recipients’ names. Use their first name if you know them, or their title and last name if you don’t. For a casual greeting, try “Hey” or “Hi.” Example: Hello, Mr. Smith and Mrs. Jones. Good afternoon, Martin and Dana. Hey Demi and Selena.
📹 Three People Who Got Instant Karma #Shorts
Three People Who Got Instant Karma #Shorts.
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.
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.
Actually, there’s a way to fairly split something between 3 people with just from 3 to 6 cuts. Explained in russian math magazine “Kvant”. Better to talk not about cake (you can use geometry to split it equally) but about 3 outlaws splitting their loot. It may be money plus clothes and other stuff which cannot be simply equally split.\r \r So, first how to split it between 2 persons so that nobody has excuse to complain. The first person splits loot into two halves which seem equally valuable for him and the second person chooses the half seems more valuable for him.\r \r Second, splitting between 3 persons. The first person splits loot into 3 parts which seem equally valuable, as before. Then second and third persons choose most preferred part and least preferred part. There may be three options.\r \r 1. Second and third persons like to take different parts. Then they take these parts and the first person takes the last part left. Each one is happy.\r \r 2. Second and third person dislike the same part. Then this disliked part is taken by the first person. Left two parts are joined and divided anew between second and third person using described above rule for two people. Everyone’s happy.\r \r 3. The most complicated case is when second and third persons like the same part and dislike different ones. We may sort parts by their appeal for each one of them (first is most preferred, last is least preferred). The second person may prefer 1-2-3, and the third may prefer 1-3-2 (other variants would be the same after renumbering).
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?
Here’s another simple solution if you don’t have a protractor: Use a tailor’s measuring tape. Mark the center of the circle of the cake. Then run the tape around the outside of the cake to measure its circumference. Divide the circumference by 3 which will give you the arc size of the back of each slice. Use that arc measurement to mark off the three points along the outside edge of the cake and then just use your knife to cut from each outer point to the center.
Another solution with no protractors or measuring tapes required: Lightly mark the outer edge of the cake with your knife at regular intervals of one blade width, counting each mark as you go. When you’ve completed the full circle of the cake, your count is a measure of the circumference of the cake in blade widths. Just divide that number by 3 then use the resulting number and the marks on the outer edge to know how many blade widths wide at the outer edge, each slice should be. Better yet, when baking your cake have some kind of regular pattern at the outer edge that you can use for measuring the cake’s circumference and know the measure in advance so when it’s time to cut the cake you just divide by the number of eaters and measure the result on the pattern to know where to cut.
Great article! Cake-cutting is such a nice problem! Note though that the method presented is NOT the envy-free Selfridge Conway method. In the Selfridge-Conway method, it is the trimmer Bob that should cut the trim and pick last. In particular, the method presented here seems proportionally fair but not envy-free. Indeed, while “Alice got an extra bit”, so did Bob, especially if Bob first got an untrimmed piece. This means that, in the end, Alice still might envy Bob’s share. More details in the Quanta Magazine article “How to Cut Cake Fairly and Finally Eat It Too”.
You can reduce the number of cuts required for 3 people from 5, as shown in this article, to 4. “A” cuts twice, leaving 3 parts: X, Y and Z. B chooses 2 favorites (Y and Z) and trims the bigger one (Y), as in the article. C cuts the trim into 2 pieces and distributes them onto Y and Z, trying to make them equal. So far 4 cuts. Now C can decide: He either takes X, or declines in favor of Y or Z. If C takes X, then: — B gets Y, and the appendix ox both Y and Z. — A gets Z without appendix, which he considered fair in the beginning. If C does not take X, then: — B gets to choose Y or Z. He has first choice and is happy. — C gets the remainder of Y and Z. He distributed, so he is happy. — A gets X, so he is happy. This is effectively a recursive algorithm. Consider 1 person and the rest, make one cut, the repeat with the remaining pieces and remaining persons.
1) Add four scoops ice cream to cake 2) Liquefy mixture in blender until homogenous 3) Distribute evenly between three similar glasses by apparent volume 4) Measure mass of each glass’ contents 5) Use pipette to closer approximate equality by weight 6) Freeze liquid 7) Break glass, remove, discard 8) Cut each frozen cakecream cylinder into nine even portions by thickness 9) Distribute disks between group, cycling (as would a poker dealer) to mitigate random error through even distribution of slice discrepancy 10) Disregard the fact that step #8 poses inherently the same problem as does the original 11) Add cakeshake slices to new glass 12) Thaw, serve.
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point, everyone will be already so bored they will not care what you do with the remaining atom of cake.
This is actually of significant importance, not because of cake but more important things. What if three siblings are to divide the household possessions of their deceased parents? Or nations are negotiating a treaty? An equitable division does not necessarily involve dividing something into quantitative equal or measurable amounts. Nicknacks, land, resources can also be divided in this way.
I’m pretty sure that this problem was solved in one of Martin Gardner’s books (at least 20+ years ago), but I can’t recall which one. As I recall, it started with one person moving the knife across the cake. Anyone can say “cut” when they would be satisfied with the piece cut off and take that piece. The remainder of the cake would be divided by the remaining two people using the one cuts the other selects solution. If the first person moved too far before the cut, the others would feel cheated and therefore would call cut before that happened. According to Gardner, the method would work for N people wanting to share a cake, just repeat the procedure with the N-1 people that haven’t gotten a piece of cake yet.
So, let’s say Charlie takes the “Dud” piece, then, Bob, seeing the trimmed and untrimmed slices as being equal, takes the untrimmed piece, would that not make Alice unhappy due to getting a piece with some cake trimmed off? Or is that in the rules, Bob must take the piece he trimmed if it is available?
Get real! Here is a normal, practical person’s solution: – Cut the cake into quarters (in half, then half again). Only a person with no sense of proportion could mess this up. – The three people get a quarter each, and the final quarter is laid on its side and cut into three pieces. Any errors on cutting the final quarter into three will be so minimal that nobody will mind. Simple. That’s the difference between an engineer and a mathematician!
This could be done in N cuts. The requirement is not equal parts, but the perception of “fairness of size and choice”. So person 1 makes the first cut to the centre then slowly moves the blade radially revealing a bigger and bigger portion. The first of person 2 or 3 to say “stop!” (Or hit a buzzer) gets the slice cut at that point. In this way it may not be exactly 1/3 but they are happy to get it, and reached a point they didn’t want to risk losing it. The person who gets the first slice now takes the knife and slowly moves the knife revealing a bigger and bigger piece while the remaining people (person 1 and 3) are vying to yell “stop” when they are happy with the portion. This extends to n people. Though the buzzer have to be more precise than jeopardy. And go really slow with the knife!
I’ve watched game shows where three people win a collective 100,000K. This basically breaks down to 33.3 recurring so it’s absolutely impossible to distribute that money equally. There has to be someone getting shorthanded. Hopefully the studios don’t round it up or down because that would just be wrong.
I accidentally fell upon this upload after hearing someone describe the essence of the Constitution. Basically saying the American Constitution was very much thought up and created in such a spirit or manner . The spirit of the Constitution Was Written In fairness. Fairness for all. ie: the spirit of the Constitution is as if one person cuts the cake and another chooses the piece. Ensuring equal portions for all sides. Such a simple idea but I find it extremely profound
Hey, here is another solution: Cake sliced into 3 ~equal pieces. Than Alice, than Bob than Charlie choose one piece. Than everybody who thinks that his piece is smaller can cut other’s person piece, take bigger cutted piece to himself, leaving his old piece + smaller cutted part to this person, then reply this process until everybody is satisfied. And it works for n-persons problem also
In theory yes, but in practice people will not manage to cut equally, they will be all confused by whats going on, a lot of the cake will be wasted in crumbs, and they will end it will different portion sizes… They will just be less satisfied than if they just cut into 3 parts and let the ones that didn’t cut choose first.
Thats a bit how we divide drugs but its usually between 2 and goes like this: 1 person cuts and the other chooses. This way both are happy because the first cut it to what he thought was even so he shouldnt care when the second person chooses what he thinks is the bigger piece. Keep this in mind when having to share something as this is the best way to do it.
from my practical insights it’s awkward to cut a circle into 3 pieces but it is easier to cut it into 6, like they cut pizza, and then everyone gets 2 pieces each. But yeah nah if its cake we are talking about it should be divided by mass not by top view area, cause it never gonna be perfect all around, if its apple pie then one piece is gonna have more apples in it and so forth
Isnt it easier for the first child cut the cake into 3 pieces, the second one choses to pieces and cut each in half, then the third child choses either the big piece or 2 among the smaller 4. Then the second child goes again and choses his piece. Lastly, the first child gets what is left. 5 cuts and 6 rounds. Done.
Here’s another solution I heard about: one person slowly moves a knife across the cake and anyone (including the person with the knife) can shout CUT at any point and the person with the knife will cut the cake, giving the slice to the person who shouted it. This works because the longer you wait, the bigger the slice is but other people will shout if you wait too long. You repeat the process until the cake is finished.
If you’re gonna go through all that effort, just measure the circumference, divide the total by how many people and cut at that interval. Ex- Cake is 42″ in circumference, you will make 3 cuts for 3 pieces at 14″ intervals around the cake. Of course make sure you’re cutting to the exact center and not at some weird angle.
The way that I’d do it it something I do in minecraft to evenly split into thirds. Everyone knows how to half something. So what you do is; 1) Cut it in half 2) Cut the bigger slice in half again and give that to the smaller slice. 3)Repeat until happy 4) the next time you half it you should have the 2 pieces you just sliced and one other piece. All 3 pieces are the same size.
I always wanted to be the chooser. You never get the perfect piece when you’re the cutter, but that’s exactly how my sister and I always divided anything growing up. One cut, the other chose. The problem was, we both wanted to be the chooser. Nowadays in my early 40’s, I’d just go for the smaller piece anyway, haha.
Better method: Instead of setting the trimming aside, why not trim piece#1 until it is equal to (piece#2 + trimming)? Then, the first eater can choose either the trimmed piece or the 2nd piece with the 1st’s trimmings, the second eater will get the remaining of those two options, and the initial cutter will get the last piece. Then, there’s no trimming left behind to deal with, saving time and mess.
Cute idea for a article, but if we are going to take it seriously, this article hasn’t taken into consideration loss aversion (check out Kahneman or Ariely). Also, logistically speaking, there is a lot of touching-of-cake going on and destroying of aesthetically-pleasing slices. Also, let us not forget the time sensitivity of freshly-baked pie or cake! In the end, the algorithm is fine for odd numbers. and I suppose even numbers that aren’t powers of two. Still, pretty cumbersome. Maybe just make another cake 🙂
I would just cut 4 pieces and leave one which will be cut afterwards. Repeat this until your cake is so small it doesn’t even matter anymore who gets how much. The problem I have with this method in the article is that a person can change its opinion during the process and the even bigger problem is that the first person has to cut it in 3 different parts anyways which could end up being messy (because it is so difficult to do it perfectly) which leaves a lot of correction work so the first person is actually happy with the seperation. Afterwards it gets even more crumbled and then it’s just getting messy.
Maybe I´m missing something, but wouldn´t it be better if the first one makes two cuts, the second one makes the third cut, the third personen chooses a piece, the first person chooses the second and the second personen chooses the third piece? Please tell me if I´m wrong, but that way sounds more efficient to me…..
The order needs to go back to Alice after Charlie. Otherwise the following may happen: Alice has never used a knife and cuts the cake into three pieces; 1/8, 1/8, and 3/4. Bob devises a plan and cuts the 3/4 into two pieces of 1/2 and 1/4. Charlie, realizing Bob’s plan, chooses the 1/4 and cuts the left over bit of 1/2 into 1/8, 1/8, and 1/4(1/4, 1/4, and 1/2 of the remaining piece). Bob then chooses the 1/4 and Alice is left choosing between one of two 1/8 pieces leaving Charlie with the remaining 1/8. In the end Bob and Charlie get 3/8 each and Alice gets 2/8.
Fair cutting method, works for an arbitrary number of people. Person A cuts a piece. Person B chooses whether to pick or pass If they pass Person C chooses whether to pick or pass If they pass Person A has it Person B cuts If they pass Person C chooses whether to pick or pass If they pass Person B has it Person C has the final piece. By going last and being forced to take the piece they cut, A is forced to try to cut an even piece because they know it’s the most they will get. If they make it bigger than a third, either B or C will take it.
The article method is in reality not fair since it takes considerable skill to cut a cake (or a piece of cake) into three equal pieces, therefore whoever must do this is at a disadvantage to those who will not need to make such a judgement. Ideally we would like everyone to be making the same judgements too! Here is a more fair method (which also doesn’t involve chopping off tiny bits of cake): A cuts a slice of cake (piece 1). B and C can take or reject the piece 1 (all three people must make the same judgement of what a third is). If both B and C reject piece 1, A takes the slice, and B and C share the remaking cake (B cuts and C chooses, which I will call “cut-choose”), again making equal judgements. If either B or C want piece 1 they take it, and the remaining two people cut-choose the remaining cake. If both B and C want piece 1, they cut-choose it, then A cuts the remaining cake into two new pieces. B and C choose which new piece they prefer. If they choose the same piece they cut-choose it, and A takes the remaining piece. If they choose different pieces they each cut-share their preferred pieces with A.
I think this was a mathematical olympics question in Saxony, 1998. According to the committee, a handful people solved it completely and the others didn’t even get a handle. I believe the crucial realization was that you can start the process over with an already cut piece. That was not allowd explicitly in the assignment, they just handwaved around the two-people example. Maybe more students would have succeeded if they had to pour some liquid or even distribute a pile of gold, as you really wouldn’t do that to a cake. P.S. I didn’t get that assignment personally, but it was the big talk right after.
There’s one scenario where this doesn’t work. If Bob cuts very large part insted of just small trimming, he still gets a big piece but Alice will get only the rest small piece. Then the ‘trimed part’ will be enourmous but Bob gets the first choice again. He can essencialy always get ~1/3 + almost 1/9 from trimed part meanwhile Alice will get only 1/9 from trimmed part and ~0 from regular cake.
Easier way: Person 1 cuts it into 6 pieces as equal as they can guesstimate, which should be pretty close since you can make 3 straight cuts through the center,. Then have person 2 and 3 alternate picking 1 pieces each until they both have 2 pieces, and the cutter gets the last 2 pieces. Bob’s your uncle.
The solution to this is so easy: There are 360 degrees in a full circle. So to divide a circle equally in 3 you just divide 360 by 3 which gives you 120. So each slice of cake should make a 120 degree angle at its apex. Now take your knife and mark the cake lightly across its diameter twice, each mark being perpendicular to the other to form a full, symmetrical cross centered at the center of the cake. Next, get a clean protractor and position its origin at the center of the cross and mark off the 120 degree point on the outer edge of the cake. You cut the cake from that mark to its center and along the corresponding limb of the cross giving you your first equal third portion. Then you just cut the remainder of the cake in half to give you your other 2 thirds (or you can use the protractor to measure another 120 degrees if you’re such an obsessive stickler for accuracy).
There is a simpler algorithm for fair cake dividing that takes just n^3 cuts. Start with one person having all the cake. Suppose the cake is fairly divided between n people. If n people have cake so far, get each of them to split their cake into n+1 pieces. And get the next person to take one piece from each. The cake is now fairly divided between n+1 people.
Isn’t this just unnecessarily complicated? A cuts cake into 3 pieces, and by definition is happy with any piece B can redistribute any amount of cake from any piece to any other piece, and thus is happy all pieces C gets to choose first, so they pick “best piece” if there is any A picks next, and is by definition happy with at least one of the remaining options B picks last, and since they did the last distribution, they must be happy with any outcome