pigeon hole principle?

[edgy frigate]

hi guys im just a bit stuck on this question i dont know where to start

[edgy frigate]

i have a slight feeling its the pigeon hole principle but i dont know how to apply it

[plucky barn]

Yeah it is, the idea here is that your "pigeon holes" should be the different pairs you wrote up

So 10 11 is one pigeon hole, 4 17 is another

can you see how to go from here?

[edgy frigate]

thankssss

wait so would it be like

i have to pull out 10 pairs or something

[plucky barn]

not quite

[edgy frigate]

im so confused

[plucky barn]

You only need to get 1 pair right

[edgy frigate]

yes

[plucky barn]

the second you have both cards in a pair you win

what's the minimum number of cards you need to pull out to ensure you have both cards in some pair?

[edgy frigate]

Wait do i need to pull out 11 cards

[plucky barn]

do you see why?

[edgy frigate]

would the 11th card be the partner of one of the 10 cards i chose

[plucky barn]

Yeah that's basically it, you have 10 different pairs, and even if the first 10 cards you pick belong to different pairs, the 11th then has to belong to the same pair as some other card

[edgy frigate]

omg thank u i need to do more pigeon hole questions tbh

i just have one more question im having trouble w

whats wrong w my answer for C

its wrong but i dont get how to do it idk where to start

i just subtracted where all teachers r next to each other to the total amount of permutatioms

[knotty oracle]

ur method doesnt countfor two teachers being next to each other

so i think you should count that as well

[abstract stratus]

yes subtract these too

[orchid mulch]

normally i just count the number of possible arrangements

[abstract stratus]

ye this question can be done using 'gap method'

[rich jacinth]

I think the trick is to

is to order it like this

{{1,19},{2,18},{3,17}...{9,11},{10, null}}

Hence if you have 10 pigeon holes, you are guaranteed to pick a number from each one of the subsets

hence if you have 9, then you are guaranteed to get one extra number in one of the pigeon holes

doesn't tip it over 21 though