# Talk:Pigeonhole Principle

Pictures will be so cool for this one! Richard 6/29

Phoebe 18:35, 8 July 2011 (UTC)Yeah, I realized that too. I'm not finished with this page yet, so I'll work on it! Thanks!
Ps: We have pretty much the same font color~ lol

## Contents

Richard 7/8

• This page is really really cool. You've got a ton of opportunities for applications and pictures.
• I'd make you Interesting Applications Section a "Why It's Interesting" section. I think this is more standard for math images. You can go to the edit with form tab to start that section.
• You really only use examples to go into the topic. Is there some graphical proof or derivation that you could include?

Phoebe 21:06, 8 July 2011 (UTC)

• First of all, thank you for leaving comments!! I use a different color to distinguish us.
• As you can see, I intend to use those 10 examples to lead in, giving readers a basic idea of what Pigeonhole principle is and how it works. The principle itself is pretty self-explanatary, so I didn't include the proof of this principle. Then, after you know how this simple principle helps in daily life, you will see the MME section with more examples and tricks about constructing pigeonholes. This is how I conceive this page, from easy to hard, from the description of pigeonhole principle, to applications (lead in), and eventually the hardest part, MME. So do you think I should put the applications under "Why interesting" after MME? If so, I'm afraid readers will feel overwhelmed by MME section. What do you think?
Okay, I see what you mean and I understand where you're coming from. To me, this page starts out with a very intuitive topic/description, and then gets more complicated in the current MME. What if there were some middle ground? I'm thinking like describing what average value is mathematically or something to put at the beginning of the MME to sort of segway into harder examples. There's a lot of examples on this page, and as the reader, I think it gets to be more difficult to pick out which examples are the most important ones. I don't know.... Richard 7/12
Richard! Check this out. I want some simple and interesting examples to lead in and I also want to put some hard applications under "why interesting" as you suggested. So, I'm thinking about splitting them into two sections, leaving the first 4-5 examples where they are now and put the rest of the examples after MME. Plus, those ten examples seem to be really long together. And people could apply those tricks mentioned in MME to see how the tricks work via the hard examples at the end of the page. What do you think about this idea? :) Phoebe 20:38, 13 July 2011 (UTC)
• Pigeonhole principle is basically about combinatorics, about numbers. This principle itself doesn't have much to do with pictures. I agree with you about the pictures. I personally like graphs than simply words and numbers, so I'm thinking about adding more illustrative pictures on it.

• Phoebe, this page is looking great! I can read it through again if you want me to, just let me know when it's ready! Richard 7/12
• Phoebe 03:16, 14 July 2011 (UTC) Yeah actually could you read it through one more time, please? Tell me where I need to explain more precisely. Thanks a lot!

# Intro

Richard 7/8

• I'd reorganize this paragraph to something like this:
A pigeon is looking for a spot in the grid, but each box in the grid, or pigeonhole, is occupied. Where should the poor pigeon on the outside go? No matter which box he chooses, he must share with another pigeon. If all of the pigeons fit into the grid, here is definitely a pigeonhole contains more than one pigeon. This concept is known as the pigeonhole principle.
• I think it's important to introduce the topic here in this section(I added a sentence at the end in my edit above).

Phoebe 21:05, 8 July 2011 (UTC)

• Agree. Fixed it!

# Basic Description

Richard 7/8

• In the first sentence, change "items" to "pigeons" or vice versa for consistency.
• In the second paragraph, I think that this quote is more confusing than helpful. I feel like you generalizing the same thing in your own words would be waaaaaay more helpful.
• It might be helpful to define "average value" and "maximum value" (maybe with a green mouse-over)
• I'd delete "Although the two versions look very different, they are mathematically stating the same thing." and into the next paragraph, "To know why they are the same," and start with "Consider the main image instead". I think it's unnecessary to say.
• Maybe change "bigger" to "greater"???? That sounds more mathy to me.
• What's "its" referring to?
"Thus, its maximum value should be bigger than one as well, which means that there must be a pigeonhole contains more than one pigeons. Now we know that the two versions are actually talking about the same math principle."
• Be careful with words like "pretty obvious". You're assuming a lot of the reader.
• Move the sentence "Here are 10 exciting real life applications listed from easy to hard for you to have a better grasp on this famous principle." into the next section before the first example.

Phoebe 21:24, 8 July 2011 (UTC)
• You have a lot of good points. I totally agree with you.
• Fixed all of them. Are they better now?

• Rebecca 02:35, 16 July 2011 (UTC) Phoebe, I'm Becky and I give feedback on many of the Math Images pages. I have a few suggestions for this page...
• I would include mouseovers for "non empty" and "finite" because I think that if someone doesn't know what a maximum value or an average value is, they wont know either of those words either.
• It's great that you introduce the general pigeonhole principle and then use explain the implications for the image. It's a logical order, and I think your approach is great!

# Interesting Applications

Richard 7/8

• This section is awesome awesome awesome.
Phoebe 23:04, 8 July 2011 (UTC)Thanks!
• Pictures would be really super cool here. The way its formatted right now makes it seem longer than it actually is, especially with the table of contents. One way that I'd think to format this is like the "More than just shadows" section of Solving Triangles. Assign a picture to each example, and make two columns where the picture and text alternate sides. The picture doesn't have to be super complicated. The birthday one could just be a cake or something. Make it look more visually appealing.
• This will also help the table of contents because you'd have to make each of the ten headings just bolded words, and not section titles.
Phoebe 21:27, 8 July 2011 (UTC)Guess what! I'm thinking about the same thing!
• Some of the example descriptions get a bit wordy. For the purposes of these comments I'll just talk about the first one as an example and then say which ones were more confusing.
• For the birthday one, you could make it more clear by changing "Under the worst condition when the first 366 students have their birthdays from January 1st to December 31th, the 367th person has to be born on any day of the year. Thus, there are definitely two of the students who have their birthday falling on the same day." to "Under the worst condition when each of the first 366 students have their birthdays on different days from January 1st to December 31th, the birthday of the 367th person must be a repeat of one of those days. Thus, there are definitely two of the students who have their birthday falling on the same day."
Phoebe 22:34, 8 July 2011 (UTC)Yeah, yours is waaaay better.
• Numbers 5 and 9 could be a lot clearer with good pictures.
Phoebe 23:03, 8 July 2011 (UTC)Add some pictures.
• Number 7's main statement is confusing to me.
Phoebe 23:13, 8 July 2011 (UTC) Could you please be more specific about it?
I understand what you are trying to prove, but I think the statement is wordy. What if you say something like: " Some n number of people are at a party. There are always at least two people who shake hands with the same number of people."? But even with the way I worded it...It' awkward. Richard 7/12
• I really like how you relate this one back to the pigeon/pigeonhole metaphor.
• Phoebe 23:03, 8 July 2011 (UTC) Thanks. I though it may be easier to understand if I do this.
• Number 8 is very confusing. That's the only one I don't understand.
Phoebe 23:55, 8 July 2011 (UTC) I made some changes. Try to make it as clear as possible.
I'm still a bit confused by this. If he has to take at least one aspirin a day, does he take 14 consecutively in a period of 14 days? I think that's where I'm confused. What statement are you trying to make? Also, where did you get 59? Richard 7/12
That is one possible answer. But he could also take 14 aspirin in less than 14 days, say he could take 14 aspirin in only 3 days. In other words, if he wants to try to avoid taking 14 aspirin during certain period, he can't do it. He may avoid taking 15 aspirin during a period of consecutive days. However, this statement is trying to say that you can always find a period of consecutive days where he takes exactly 14 aspirin. Am I being clear enough or not? Please ask me more questions if you are still confused. :P
How did I get 59? Since you add 14 to every term in the first inequality, you'll get 45 + 14 = 59 for the very last term.
Maybe I could generalize this statement instead of using numbers 45, 14, 30. (i.e. he has to take $n$ aspirin over a $m$ day period. Then there is definitely a period of consecutive days where he takes exactly $n - m -1$ aspirin.) Do it make more sense now?
• Number 10a is awesome! Great, clear description!
Phoebe 23:55, 8 July 2011 (UTC) Good to know. Thanks!
• For 10b, I didn't know exactly what you you were trying to show until you had already started to prove it. This one might be in need of some more clarity in the initial description of the proof and statement.
• Typo:"situation" should be "situations" in "Since there are over 32,000 possible colorings, we could not draw and check every one of the situation."

# MME

## More Mathematical examples

Richard 7/8

• Number 1 is confusing.
• For number 2, wouldn't it just be easier to choose all of the odd numbers, knowing that they are not consecutive and that there are only 50, then we know that the 51st must be even and next to an odd number.
Phoebe 02:10, 9 July 2011 (UTC)Yes, you are right.

## How to Construct

Richard 7/8

• I was a bit confused by these examples.
• This might also be a good point to derive or prove the principle explicitly with the math for average and maximum values????
Phoebe 03:09, 9 July 2011 (UTC) I tried to fixed those confusing examples. Maybe some of them are still not very clear. I'll work on them later. Please feel free to tell me where should I improve. Thanks!