Meep's Math Matters 8: The Pigeonhole Principle

In the 8th episode of Meep's Math Matters, I introduce the pigeonhole principle and cover three applications of the principle. I give a little homework (seriously, it's just for those who want to try out the principle...I will be giving the answers in a followup episode), and a neat bit of trivia you can break out at your next party to prove what a math geek you are.

I can be contacted at marypat.campbell@gmail.com, and spread the Math Love! (It's contagious!)

Category:

Education

Tags:

• math
• classic
• geometry
• triangle
• pigeonhole
• principle
• socks

[siripala911]

Hi, is it possible for you to tell me how to work this out.. A is a set of integer with #A =67. Show that atleast 7 have the same remainder when divided by 11

[meepsmathmatters]

@siripala911 I'll get you started -- how many different remainders can there be if you divide by 11?

[meepsmathmatters]

@meepsmathmatters the answer to that will be your number of "pigeonholes" and then your 67 integers are 67 pigeons.

[0x1234]

I was wondering if you knew how to do this questions:

A box contains 10 blue ice-cream sticks, 20 red ice-cream sticks and 25 purple ice-cream sticks. How many must i choose to ensure that 12 ice-cream sticks are of the same colour?

[meepsmathmatters]

here the pigeonholes are colors, and the pigeons are the sticks.You want to make sure at least 12 sticks are in each box.

So you think of the most sticks you could cram in each box without there being 12 in any of them.... and then add one more.

Good luck with your homework.

[0x1234]

Thanks:)

[meepsmathmatters]

Ooops, a little early for me with the DST. What I meant was that you need to make sure there's at least 12 sticks in at least one box (not in all 3 boxes).

Keep in mind that the blue ice cream sticks are throwing you off -- there's only 10 of those, so there can't possibly be 12 of those to choose. Nice tricky twist on a standard pigeonhole principle problem.

[wynz24]

@meepsmathmatters hi, can u help me with this question?

What is the minimum number of students, each of whom comes from one of the 50 states, who must be enrolled in a university to guarantee that there are atleast 100 who come from the same state?

[meepbobeep]

@deszczyn note - i cover the 0 hairs possibility....

[deszczyn]

what about people with cancer... they don t have hair

[fashionistagal01]

i got this for my project but i still dont get it!!! wad do u mean by

'So you think of the most sticks you could cram in each box without there being 12 in any of them.... and then add one more'???

[0x1234]

I think the answer should be 50 right? There is another question which doesn't make much sense to me.

Each of the 40 participants in a workshop signed up for one or more of the following courses; Handicraft,Ceramics and Chinese Paintings. How many participants signed up for the same courses?

Then wouldn't the answer be all 40 since there are only 3 choices?