Meep's Math Matters 8: The Pigeonhole Principle

[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.

[deszczyn]

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

[meepbobeep]

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

[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?

[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?

[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'???

[guivyse]

nice video,

but think a little more,

you will see that there arent only 2 people with the same number of hair, in the USA, but at least 34 people,

using your numbers

[meepsmathmatters]

Correct.

My point wasn't to make the strongest possible statement I could. This does happen a lot in math - you just want to prove the existence of a solution to a particular problem, say, but don't care to be bothered to show what that solution is. (My graduate math classes had a lot of that sort of thing going on.)

[Hotmonkeylovin]

I would divide one pigeon into four so each hole will have 1 1/4 pigeon in it. (he, he)

[meepsmathmatters]

Hey, I'm all for thinking outside the pigeonhole.

[Hotmonkeylovin]

(Wow you responded!)

I am an ammature mathematician; that is to say I'm trying to learn advanced math (pure mathematics) on my own by starting from the begginning to the advance progessively (sadistic huh?). I don't really know where to start but your video is very informative.

I would appreciate any advice. Thank You.