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# UKMT Intermediate Olympiad 2016 watch

1. Hi everyone.
Earlier today I did the Cayley Olympiad - just wondering how everyone found the Cayley/ Hamilton/ MacLaurin. Please give your solutions if possible as I want to have a general idea about how much other people agreed with me.
You can also talk about future UKMT competitions here (I'm doing the Team Maths Challenge next week) and give advice.
2. Hello,

I produced full solutions for questions 1-5 and ran out of time for 6
3. Same with me and I also did the Cayley. What answers did you put for the first five qu's? I'm also interested if anybody managed to solve Qu 6 how they did it Thanks!
PS. What are you all aiming for?
4. I got 11 for the multiples of 9; 112 or something like that for the phone number question; the top left corner is 8; Dan can't have his wish fulfilled. I didn't do the other two.
5. (Original post by lrn14)
Same with me and I also did the Cayley. What answers did you put for the first five qu's? I'm also interested if anybody managed to solve Qu 6 how they did it Thanks!
PS. What are you all aiming for?
I got a solution for question six, basically I proved that the triangle coming off the side is isosceles which means by extension that one side of the larger one is double one side of the smaller one. Sorry, that's not a great explanation! I'm hoping to at least get a medal as I did all of the questions fully- what are you hoping for?
6. (Original post by BriannaTheBreeze)
I got a solution for question six, basically I proved that the triangle coming off the side is isosceles which means by extension that one side of the larger one is double one side of the smaller one. Sorry, that's not a great explanation! I'm hoping to at least get a medal as I did all of the questions fully- what are you hoping for?
Same - I'd love to get a medal! Well done for answering all six and thanks Did you think it was an easier or harder paper than the questions last year?
7. (Original post by lrn14)
Same - I'd love to get a medal! Well done for answering all six and thanks Did you think it was an easier or harder paper than the questions last year?
I found it easier than last year's one, but that may just be due to personal preference and also thanks What about you, how did you find it in comparison? Also, do you have any idea about when the grade boundaries will be released?
8. I also got that solution for 6. Did you just join the line to the centre, join the corner immediately to the right on the large heptagon to the centre and get an isosceles triangle, label the angles x, so the interior angle of the heptagob was 2x, so the small triangle had angles x, 180-2x and so the other was x and so isosceles.. I know it's not very clear, but is that along the same lines as what you did?
(Original post by BriannaTheBreeze)
I got a solution for question six, basically I proved that the triangle coming off the side is isosceles which means by extension that one side of the larger one is double one side of the smaller one. Sorry, that's not a great explanation! I'm hoping to at least get a medal as I did all of the questions fully- what are you hoping for?
9. (Original post by BriannaTheBreeze)
I found it easier than last year's one, but that may just be due to personal preference and also thanks What about you, how did you find it in comparison? Also, do you have any idea about when the grade boundaries will be released?
Also what did you put for the first question? Thanks!
10. (Original post by TheBigBrick)
I also got that solution for 6. Did you just join the line to the centre, join the corner immediately to the right on the large heptagon to the centre and get an isosceles triangle, label the angles x, so the interior angle of the heptagob was 2x, so the small triangle had angles x, 180-2x and so the other was x and so isosceles.. I know it's not very clear, but is that along the same lines as what you did?
Yeah, that's pretty much exactly what I did, just used different variable names for the angles (I called them 900/7 as that's the fractional equivalent of the decimal value and they said not to approximate- your way sounds like it works just as well though, less clunky in fact!)
11. (Original post by lrn14)
Also what did you put for the first question? Thanks!
I'm pretty sure I got 11 for the first one
12. For the first one I got 11:
135,153,315,351,513,531,333,999, 117,171,711
13. Thanks. I liked that question, question 3 with phone number I hated though . I think that was the easiest Cayley yet though possibly, so boundaries could be tough, I just hope I dot drop marks here and there for not explaining clearly. On question 5, did you put that for it to be possibe, 2 and 6 had to go in the same row AND column for the product of all columns to be divisible by 4(which clearly isn't possible etc)?
(Original post by BriannaTheBreeze)
Yeah, that's pretty much exactly what I did, just used different variable names for the angles (I called them 900/7 as that's the fractional equivalent of the decimal value and they said not to approximate- your way sounds like it works just as well though, less clunky in fact!)
14. I said that Q5 was impossible for TheBigBrick's reasoning pretty much
15. (Original post by lrn14)
Oh no!! I put 6 :O How?
So you can have 4 distinct combinations:
1, 3 and 5
1, 1 and 7
3, 3 and 3
and finally 9, 9 and 9

You can arrange 1, 3 and 5 in six ways,
You can arrange 1, 1 and 7 in three ways.
You can arrange 3, 3 and 3 in one way,
And you can arrange 9, 9 and 9 in one way, giving:

6+3+1+1=11

I hope I explained my reasoning with some degree of clarity

How did you get six?
16. Dd people find that easier generally?
17. I found it okay as there were 4 numerical questions. I didn't like the wording of the 2016 6x6 graph questions as it said "all the numbers" which implied several answers - I only got one possible answer: 8.
18. How did you get 6 for Q1? Also do you know how they work out the marks?
19. (Original post by TheBigBrick)
Thanks. I liked that question, question 3 with phone number I hated though . I think that was the easiest Cayley yet though possibly, so boundaries could be tough, I just hope I dot drop marks here and there for not explaining clearly. On question 5, did you put that for it to be possibe, 2 and 6 had to go in the same row AND column for the product of all columns to be divisible by 4(which clearly isn't possible etc)?
That's roughly what I said, I think. It's mostly about the reasoning so as long as your argument has clarity you should get the marks.
20. Does anyone know when the solutions for the questions will be posted, and how long it usually takes for the results to come out? I know it will take quite a long time to mark them, but is it usually like a month? Or a couple of weeks because there are less papers to mark than the challenge?

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