pigeonhole principle 💔💔 (1 Viewer)

[jane1820]

i need a visualisation for this question and solution bc i cant seem to understand it (not that i understand php anyways)

 

[killer queen]

(Enjoy the triforce I just terribly drew with my finger)

there are only four triangles you can divide into so, by PHP, worst case scenario, one dot in each triangle - but you have 5 dots! So there’s still one dot left over, which has to share a triangle with another dot, hence there MUST be two dots in one triangle drawn in this method

And the furthest apart they can be is if they were at opposite ends of one side i.e. one unit apart! (You can try this in your head ) Since they’re confined with an equilateral triangle with sides of 1 unit each

sorry for the rushed explanation, hope this helps!

 

[jane1820]

omg thank you

 

[NotBamboo]

View attachment 47370
(Enjoy the triforce I just terribly drew with my finger)

there are only four triangles you can divide into so, by PHP, worst case scenario, one dot in each triangle - but you have 5 dots! So there’s still one dot left over, which has to share a triangle with another dot, hence there MUST be two dots in one triangle drawn in this method

And the furthest apart they can be is if they were at opposite ends of one side i.e. one unit apart! (You can try this in your head ) Since they’re confined with an equilateral triangle with sides of 1 unit each

sorry for the rushed explanation, hope this helps!

ZeLdA rEfErEnCe omg

 

[NotBamboo]

View attachment 47368

i need a visualisation for this question and solution bc i cant seem to understand it (not that i understand php anyways)

@killer queen
answer is wrong, it shouldnt be split into 4 equilateral triangles but 3 sectors (each having interior angle of 120°)
regardless, the answer is the same, but it wouldn't be an accurate diagram.

heres correct diagram:

 

[killer queen]

@killer queen
answer is wrong, it shouldnt be split into 4 equilateral triangles but 3 sectors (each having interior angle of 120°)
regardless, the answer is the same, but it wouldn't be an accurate diagram.

heres correct diagram:
View attachment 47373

I get where you’re coming from and yeah that’s more accurate but realistically in an exam for these kinds of questions the answer is often to divide a shape into equally sized shapes, I’ve seen similar with squares

Why do you say the answer is wrong? I see no mathematical error in it

I had the exact triangle q in my year 11 exam once and the way I answered it was the official answer as well

 

[jane1820]

I had the exact triangle q in my year 11 exam once and the way I answered it was the official answer as well

oh wow i thought that was too advanced for an exam (like the enrichment cambridge questions - u dont see them in an exam)

 

[killer queen]

oh wow i thought that was too advanced for an exam (like the enrichment cambridge questions - u dont see them in an exam)

It’s certainly a more difficult application of the pigeonhole principle but considering how many of these sorts of questions out there, I’d say it’s an ‘easy’ E4 question - you’ve seen it once, in future these kinds of geometric ones you have a clue on how to start, and maybe you’ll get the answer along the way if you know what I mean? And even if you don’t get the answer you’ll probably have picked up those initial marks

My teachers do say they make hard exams tho

(I probably need to get my hands on the Cambridge ext 1 book don’t I)

 

[NotBamboo]

I get where you’re coming from and yeah that’s more accurate but realistically in an exam for these kinds of questions the answer is often to divide a shape into equally sized shapes, I’ve seen similar with squares

Why do you say the answer is wrong? I see no mathematical error in it

I had the exact triangle q in my year 11 exam once and the way I answered it was the official answer as well

i just said the answer is the same in the post silly (being 5 pigeons in 4 pigeonholes)
its just i hate that they don't put an accurate answer cus they are thinking about it algebraically and not realistically
DIAGRAM isn't 100% right, but it's conceptually the same thing so it should be accepted and its much easier understood

ALSO GOOD LUCK WITH UR HSC

 

[NotBamboo]

oh wow i thought that was too advanced for an exam (like the enrichment cambridge questions - u dont see them in an exam)

if ts in my exam i won't even need to study anymore

 

[jane1820]

if ts in my exam i won't even need to study anymore

I would drop ext on the dot if it comes in my exam

 

[jane1820]

guys i actually dont know how to answer questions regarding the pigeonhole principle bc i dont get it, what do i do?

 

[killer queen]

guys i actually dont know how to answer questions regarding the pigeonhole principle bc i dont get it, what do i do?

Usually the answer lies in the worst case scenario, or as I like to call, what would cause me the most effort to do? If you see more questions you’ll start to see a sort of pattern with the kind of approach you have to take - for example, a super common one is if I have red, black and white socks, how many socks do I need to take out of the drawer to ensure I have a pair? Well, the most effort it would take me would be if I drew one of each colour first, before getting a second of any colour e.g. black, red, white, red. That’s the most effort it could take me, and therefore the answer is 4. No matter what that fourth sock is, it’ll HAVE to make a pair with one of the other colours drawn. So what if I want 3 socks of the same colour? Then the minimum is 7. 4 socks of the same colour? The minimum is 10. Even though though it’ll say the minimum number of socks, I know my class joked that it’s more like a maximum at least in the way the brain perceives it, because in this situation it guarantees the outcome you’re looking for.

Hope this helps!

 

[jane1820]

I just find it hard to find the pigeonhole and pigeons in a question