Pigeonhole Principle
Read this topicExplanations 6
- PigeonholePigeonholePigeonhole Principle!Principle!Principle! The Pigeonhole Principle is pretty intuitive and follows from the logical observation that if there are n boxes, in…
By Evan Tong
- Pigeonhole Principle : The Statement Credits of the image to this site. Yes, what could be easier than the observation that if we put more than nnn pigeons into nnn pigeonholes,…
By Zi Song Yeoh, Alex Federspiel
- Pigeonhole Principle : Generalized If you have ppp pigeons and hhh holes, then at least one hole contains at least ⌈ph⌉\lceil\frac{p}{h}\rceil⌈hp⌉ pigeons. Credits to this site…
By Zi Song Yeoh
- Now we are talking about a fundamental method or process of elementary number theory. I try to describe the pigeonhole principle informally at a bit rate for the first. If you a…
By অস্তিত্বের শেকড় সন্ধানী, Andrew Wang
- If nnn objects are placed into kkk boxes, then there is at least one box containing at least ⌈nk⌉\lceil\frac{n}{k}\rceil⌈kn⌉ objects, and at least one box containing at most ⌊n…
By Benjamin Qi
- Generalized Pigeonhole Principle: If NNN objects are placed into kkk boxes, then there is at least one box containing at least ⌈Nk⌉\lceil\frac{N}{k}\rceil⌈kN⌉ objects and there…
By Benjamin Qi
Problems 14
- Practical Principle I have two colors of socks: white and black. I like to wear socks of the same color, but I'm in a hurry. I'd like to grab a handful of socks all at once, so …
- I'd like to teach my first class using just one color. Fortunately, I can be sure that some color will have at least ___ markers. Fill in the blank. Please enter the biggest num…
- Then, there must be some color with at least ___ marbles. Fill in the blank. Please enter the largest number for which the statement is always true.
- If there are nnn pigeons and n+1n+1n+1 holes, then...
- How many marbles should you pick out?
- Practical Principle 2 Aragog the spider lives in the forest and his 8 feet are very cold. So he starts looking for socks. The socks in the forest have the colors red, orange, ye…
- There are nnn points marked in an equilateral with side length 222 such that there are no two points within distance 111 of each other. What is the largest possible value for nnn?
- You have 111 coin with 111 written on it, 222 coins written 222 on them, and so on for 505050 coins with 505050 written on them. How many coins must you take in order to ensure …
- What is the least integer kkk such that among any kkk integers not exceeding 2n,2n,2n, there must be two integers which are relatively prime to each other?
- There are 38 different time periods during which classes at a university can be scheduled. If there are 677 different classes, at least how many different rooms will be needed?
- What is the minimum number of students who must be enrolled in a university to guarantee that there are at least 100 who come from the same state?
- A bowl contains 10 red balls and 10 blue balls. A woman selects balls at random without looking at them. How many balls must she select to be sure of having at least three balls…
- Danny has 101 Dalmatians in 102 doghouses. If Danny were to multiply together the numbers of dogs in each doghouse, what would be their product?
- What is their table number?