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Australian Maths Competition (5 Viewers)
- Thread starter maths94
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hayabusaboston
Well-Known Member
Re: Australian Maths Competition 2013
I have photographic memory in that phase right before sleep. Also during lucid dreaming, of which I do a lot. I can visualise an event crystal clear, from months or yeeaaars ago, and just play it back in my mind, lurid as ever.
Re: Australian Maths Competition 2013
There is a proof of the AM-GM inequality published in the 1920s by George Pólya. There are many proofs of this, but Pólya's method is called Pólya's Dream.
I'm delighted that it's in the 4 unit Cambridge text book, but disappointed that they did not appropriately accredit it to Pólya.
It's called Pólya's Dream because he actually dreamt the proof!
There is a proof of the AM-GM inequality published in the 1920s by George Pólya. There are many proofs of this, but Pólya's method is called Pólya's Dream.
I'm delighted that it's in the 4 unit Cambridge text book, but disappointed that they did not appropriately accredit it to Pólya.
It's called Pólya's Dream because he actually dreamt the proof!
Last edited:
iBibah
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Re: Australian Maths Competition 2013
EDIT: Just googled it, and I think I just found a video you uploaded.
Is that you? the teacher?
Wow, that would make studying so much easier if we used sleep time lol
EDIT: Just googled it, and I think I just found a video you uploaded.
Is that you? the teacher?
iBibah
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Re: Australian Maths Competition 2013
Nah mate the answers are provided later when awards are distributed.
RealiseNothing
what is that?It is Cowpea
Re: Australian Maths Competition 2013
I know the answers for all the multiple choice if you want them.
hayabusaboston
Well-Known Member
Re: Australian Maths Competition 2013
1101101 = 29759 x 37 + 18
Five 1s are enough:
1101101 = 29759 x 37 + 18
RealiseNothing
what is that?It is Cowpea
iBibah
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Re: Australian Maths Competition 2013
Aren't most of the questions involving integers just trial and error? The only way that I attempt them is to substitute in numbers until I get the answer, although this takes a very long time.
Re: Australian Maths Competition 2013
For the 37 & 18 question, note first that 37 x 3 = 111 which seems to be heading vaguely in the right direction.
Then 999 is also a multiple of 37, so as well as 100 being 11 less than a multiple of 37, 1000 is 1 more than a multiple of 37.
Then looking just at the remainders after division by 37:
1 leaves 1 ; 10 leaves 10 ; 100 leaves 26 (effectively -11) ; 1000 leaves 1 again, so the pattern repeats:
10,000 leaves 10 ; 100,000 leaves 26 or -11 ; 1,000,000 leaves 1 remainder
Then you just need to combine as few of these remainders as possible to get an overall remainder of 18
None of the questions are ever intended to be solved by trial and error, though a bit of experimenting with numbers can often set you on the right track
For the 37 & 18 question, note first that 37 x 3 = 111 which seems to be heading vaguely in the right direction.
Then 999 is also a multiple of 37, so as well as 100 being 11 less than a multiple of 37, 1000 is 1 more than a multiple of 37.
Then looking just at the remainders after division by 37:
1 leaves 1 ; 10 leaves 10 ; 100 leaves 26 (effectively -11) ; 1000 leaves 1 again, so the pattern repeats:
10,000 leaves 10 ; 100,000 leaves 26 or -11 ; 1,000,000 leaves 1 remainder
Then you just need to combine as few of these remainders as possible to get an overall remainder of 18
enigma_1
~~~~ Miss Cricket ~~~~
Re: Australian Maths Competition 2013
Whoaaa how do you guys actually do the questions? They freak me out, legit they're like essays towards the end. Please share your techniques, or how you even approach the questions. Fannkss!!
Whoaaa how do you guys actually do the questions? They freak me out, legit they're like essays towards the end. Please share your techniques, or how you even approach the questions. Fannkss!!
Makematics
Well-Known Member
Re: Australian Maths Competition 2013
i just split it up into a rectangle and a triangle and did tan (angle) =8/(5+3+8)=1/2 and then the angles are corresponding angles and then messed around to get 55/4. sounds easier than what you did.
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Makematics
Well-Known Member
Re: Australian Maths Competition 2013
I get 714 m^2 as my answer for Q27. has anyone else got an answer?
I get 714 m^2 as my answer for Q27. has anyone else got an answer?