Sydney Tech HSC CT1 2020 10.c (1 Viewer)

[jane1820]

umm where did the 9 come from? the question says infinite number

also i tried to approach the question as:
'let n be the total number of socks'
but idk if thats the correct way bc i didnt know how to finish off, can someone answer my question abt the 9 and the question?

 

[jane1820]

chat please im stressing

 

[Study to success]

Why is she pulling out socks in the dark. Like turn the light on and she wouldn’t have this problem

 

[Hehehe22]

Have you learned the pigeonhole principle? That's what this is asking for.

Since you want to "guarantee", you have to think of the worst case scenario, which occurs when you have 9 of each kind of sock but 10 of none (9*4=36). In this case, the next sock you pull out, no matter what colour, will make 10 of that colour. Thus, 37 socks will guarantee 10 of at least one colour of sock.

Sorry if this is confusing, I'm bad at wording maths explanations. If anyone can provide a diagram that might be helpful lol

 

[jane1820]

yes i have

i think i understood what u mean but can you please give a diagram? im more of a visual learner

 

[Hehehe22]

yes i have

i think i understood what u mean but can you please give a diagram? im more of a visual learner

Sorry I can't really think of how to draw it visually, that's why I asked if anyone else would

 

[liamkk112]

View attachment 47530
View attachment 47531

umm where did the 9 come from? the question says infinite number

also i tried to approach the question as:
'let n be the total number of socks'
but idk if thats the correct way bc i didnt know how to finish off, can someone answer my question abt the 9 and the question?

think about it like this. assuming you’re equally likely to pull each color (1/4), what’s the worst scenario you could be in to delay meeting your goal? you can first draw 9 of the first color. after that, if you drew another of that color you’d be done so that’s not the worst case. then draw another 9 of the other color and so on. overall you could at most pull 9x4 socks, without meeting your criteria, since if you ever pull one more you’d be guaranteed to have 10 of the same color. hence the moment you get one more than this amount, you have been guaranteed 10 socks of the same color

 

[Legendary16]

Sorry I can't really think of how to draw it visually, that's why I asked if anyone else would

I agree with your signature