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Type: Posts; User: RealiseNothing

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by RealiseNothing
Replies
53
Views
532

### Re: UNSW Comp

I just realised for question 6, I could have written down the general formula:

\binom{2k+1}{k+1}

which would have given me extra credit marks :(

by RealiseNothing
Replies
53
Views
532

### Re: UNSW Comp

1) Prove that 'n' has to be a multiple of 2 (fairly straight forward and obvious as you need an even amount of terms so that all 1's and -1's cancel out).

2)Prove that 'n' can be a multiple of 4....

by RealiseNothing
Replies
53
Views
532

### Re: UNSW Comp

My approach:

Prove that:

2^{3^n} + 1 = p.3^{n+1}

Where 'p' is not divisible by 3.

by RealiseNothing
Replies
53
Views
532

### Re: UNSW Comp

2^{3^2} + 1 = 2^9 + 1 = 513

\frac{513}{3^3} = \frac{513}{27} = 19

by RealiseNothing
Replies
53
Views
532

### Re: UNSW Comp

Me too.

by RealiseNothing
Replies
53
Views
532

### Re: UNSW Comp

Same here, I tried to prove it with my 4 page induction :p

Came so, so close as well, was disheartening having to give up and move on as time was running out.

by RealiseNothing
Replies
53
Views
532

### Re: UNSW Comp

I was the 1st ever.

by RealiseNothing
Replies
53
Views
532

### Re: UNSW Comp

I got k=n+1

by RealiseNothing
Replies
53
Views
532

### Re: UNSW Comp

I just said "all possible combinations of 4 people from 7, ie ABCD, ABCE, ABCF, ... , DEFG"

I'm pretty sure I got question 1, 2, 5, and 6 right, with partial solutions to 3 and 4 (came so close to...

by RealiseNothing
Replies
53
Views
532

### Re: UNSW Comp

Yep.

by RealiseNothing
Replies
53
Views
532

### Re: UNSW Comp

are we allowed to post solutions?

by RealiseNothing
Replies
53
Views
532

### Re: UNSW Comp

This is what I had for question 6, I hope it's actually right lol.

Basically we want any 4 to be able to unlock it, but any 3 can not. So if we give out 4 keys for each lock, then we will have 3...

by RealiseNothing
Replies
53
Views
532

### Re: UNSW Comp

I was the first person in my school to ever do it.

by RealiseNothing
Replies
53
Views
532

### Re: UNSW Comp

I think I got question 1, 2, 5, 6 right. Hopefully anyway lol. And hoping my partial solutions to questions 3 and 4 gets me a couple marks.
15. ## Thread: HSC 2013 4U Marathon

by RealiseNothing
Replies
1,756
Views
50,878

### Re: HSC 2013 4U Marathon

So who is pumped for the UNSW comp tomorrow?
16. ## Thread: Perms and combs with probability help

by RealiseNothing
Replies
6
Views
138

### Re: Perms and combs with probability help

The denominator of the first one should just be:

\binom{8}{1} + \binom{8}{2} + \binom{8}{3} + \binom{8}{4}

By having the rest you are double counting as choosing a group of 3 and a group of 5...

by RealiseNothing
Replies
3
Views
92

### Re: Permutation

\frac{5!}{2!\times2!}
18. ## Thread: HSC 2013 4U Marathon

by RealiseNothing
Replies
1,756
Views
50,878

### Re: HSC 2013 4U Marathon

1am me wasn't thinking straight.
19. ## Thread: HSC 2013 4U Marathon

by RealiseNothing
Replies
1,756
Views
50,878

### Re: HSC 2013 4U Marathon

The area of the triangles will be \frac{1}{2} PQ.PR

So we need to find the average length of PQ and PR. Now if (n) is odd, then we can fix the point P to be the centre of the square. The average...
20. ## Thread: HSC 2013 4U Marathon

by RealiseNothing
Replies
1,756
Views
50,878

### Re: HSC 2013 4U Marathon

My solution is I can choose the point P in n^2 ways as it can take any point on the square. Then Q and R can both be chosen in (n-1) ways as they can take any point in the row or column that P was...
21. ## Thread: HSC 2013 4U Marathon

by RealiseNothing
Replies
1,756
Views
50,878

### Re: HSC 2013 4U Marathon

Yep I get the factored version first.
22. ## Thread: HSC 2013 4U Marathon

by RealiseNothing
Replies
1,756
Views
50,878

### Re: HSC 2013 4U Marathon

In that case I get n^4-2n^3+n^2

If this is right I'll post my solution.

edit: I just tried a different method and got \frac{1}{2} (n^4-2n^2+1)

Not sure if either of these are right or why I...
23. ## Thread: HSC 2013 4U Marathon

by RealiseNothing
Replies
1,756
Views
50,878

### Re: HSC 2013 4U Marathon

By different triangles, do you mean triangles with different co-ordinates as their vertices or triangles which are not congruent to each other, or they can be congruent if they are rotated?
24. ## Thread: HSC 2013 4U Marathon

by RealiseNothing
Replies
1,756
Views
50,878

### Re: HSC 2013 4U Marathon

Pairwise distinct integers just means that the integers are distinct with respect to one another I think. Simply put, you can not use an integer between 1 and 100 more than once.
25. ## Thread: Lose Marks for writing over lines?

by RealiseNothing
Replies
8
Views
405

### Re: Lose Marks for writing over lines?

~HSC science~
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