Australian Maths Competition 2012 Thoughts (1 Viewer)

[iBibah]

q29 was the terryfic list
and sorry to break any bubbles but q26 aint 200

Here is working through algebra I did for someone (if not done by logic).

 

[nerdasdasd]

Zzz I probably failed ... Couldn't do quite a bit of the paper ..

 

[Thief]

Guys courier question, I got 225.

 

[RealiseNothing]

Guys courier question, I got 225.

Yep, fuck, it's this, thief just showed me the working out.

/fml.

 

[Thief]

Will attempt to show you guys the working on bos

 

[twinklegal19]

Yep, fuck, it's this, thief just showed me the working out.

/fml.

ahahahahaha

Good job thief

 

[Thief]

For all you guys saying 200, you are noob (hehe I beat Realise at maths).

So my theory was, that because the aim of the question is to find maximum distance, you'd need one person to go as far as they can by themselves in order to save fuel.

ie: The pair will travel to a certain distance, and then person A will help person B refuel. B will then travel 150km to the destination by themselves and back (as 300km is the max capacity of the fuel tank).

That means that there is 300km fuel remaining to be shared between person A and B travelling to the refuel point and back.

300/4 = 75
75 + 150 = 225km

 

[iBibah]

For all you guys saying 200, you are noob (hehe I beat Realise at maths).

So my theory was, that because the aim of the question is to find maximum distance, you'd need one person to go as far as they can by themselves in order to save fuel.

ie: The pair will travel to a certain distance, and then person A will help person B refuel. B will then travel 150km to the destination by themselves and back (as 300km is the max capacity of the fuel tank).

That means that there is 300km fuel remaining to be shared between person A and B travelling to the refuel point and back.

300/4 = 75
75 + 150 = 225km

haha well done

Would someone be able to find a flaw in this then:

Say it is 225km away. Person A travels there, and then manages to come back 75km before he is out of fuel. Therefore he has 150km to go. B comes 150km and gives 150km to A to get back. That means B has used her 300km of fuel and can't get back.

 

[Parvee]

haha well done

Would someone be able to find a flaw in this then:

Say it is 225km away. Person A travels there, and then manages to come back 75km before he is out of fuel. Therefore he has 150km to go. B comes 150km and gives 150km to A to get back. That means B has used her 300km of fuel and can't get back.

-If Person A and Person B travels 75km, they both have 225km fuel left.
-Person A transfers 75km of fuel to Person B. Person A now has 150km of fuel while Person B has 300km.
-Person A waits at the same spot while Person B travels 150km to the destination and 150km back to the place the transferred fuel.
-Person A transfers 75km fuel to Person B. They both now have 75km of fuel to get back to starting position.
-Therefore 225km distance to the destination.

 

[Demento1]

Yep, fuck, it's this, thief just showed me the working out.

/fml.

Don't worry too much about the question, we're all human. Was the courier question, Q 26. in your paper? You could still possibly get a HD after this error as I did the senior paper you guys did and I couldn't answer like 8 questions.

Guys courier question, I got 225.

Good work.

Was the question 29 the same in the year 10 paper too?

Mhm, I think I managed to solve that question and it was Q30. in the intermediate paper.

 

[jason2kool]

easy HD, nwz

 

[iBibah]

-If Person A and Person B travels 75km, they both have 225km fuel left.
-Person A transfers 75km of fuel to Person B. Person A now has 150km of fuel while Person B has 300km.
-Person A waits at the same spot while Person B travels 150km to the destination and 150km back to the place the transferred fuel.
-Person A transfers 75km fuel to Person B. They both now have 75km of fuel to get back to starting position.
-Therefore 225km distance to the destination.

Yeh I get this way. I was just under the impression that no matter how you send them the max distance wouldn't change. That's why when I did it I sent one of the as far as possible and back. Then the other came and retrieved them. When done this way the max was 200.

 

[RealiseNothing]

Wellll fuck.

Just realised question 29 isn't 225.

There goes all of my last 5 questions.

 

[iBibah]

Wellll fuck.

Just realised question 29 isn't 225.

There goes all of my last 5 questions.

haha chill, what was q29?

 

[NitroFatez]

well, so whats the ans for qs 30 for year 7,8 paper or qs29(its the same question) which appeared in the yr 10 or smth paper ._.
currently i already had quite some marks deducted considering that i got it wrong for the questions im unsure in...

 

[RealiseNothing]

haha chill, what was q29?

It's like 9 or something.

 

[hayabusaboston]

NitroFatez reminds me of Need For Speed Hot PUrsuit. ANyone wanna race me online??

 

[tankz]

Can someone upload or tell me from where i can get the 9-10th grade paper?

 

[tywebb]

The intermediate paper is at http://www.mediafire.com/?khhaskz0oxp4xca

 

[sdort]

Yea i heard it was 9 as well, no idea how though
You have working out?
Also anyone who got q30 plz explain

For the Terryfying list question, the list is built as so:

[0][1,2][1,2,3,2,3,4][1,2,3,2,3,4,3,4,5]...

This shows that nth list ends in 3^n-1.
So we locate where 2012 is, which is between 3⁶(=729) and 3⁷(=2178)

As the rules suggest, the 1st - 729th numbers is repeated twice, and each repeats adds on a value of one to the whole list. Thus, 730th-1458th and 1459th-2178th numbers are the same numbers as 1st-729th numbers, but with values of 1 and 2 added respectively.

Thus, we find what 2012 is what ordinal number between 1459 and 2178. (2012-1458 = 554th number).
And so, 2012 is the same as the 554th number +2.

We repeat the process:
[1-243][244-486][487-729]
Where 544 is the same as 68th(554-486) +2.
[1-27][28-54][55-81]
Where 68 is the same as 14th(68-54) + 2
[1-9][10-18][19-27]
Where 14 is the same as 5th(14-9) + 1

And from the original given list, the 5th number is 2.
So the 2012th number is 2 +1+2+2+2 = 9.