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UKMT Maths Competitions Thread

Welcome to the UKMT Maths Competitions Thread. I've created this as an area for people who are interested in these competitions to openly participate and collaborate on problems.

Each year different threads are created for different competitions, and I thought it would be best to unify such threads into one.

I ask that anyone who posts a problem specify its source, the question number and the year it was posted i.e (BMO1 Q1 1996)

Also please use LaTeX when typing out the maths. There's an intro to LaTeX here: http://www.thestudentroom.co.uk/showthread.php?t=403989

Feel free to post problems from other countries' olympiads and sources that are not affiliated with the UKMT.

Past Papers and Problems to try out

If someone is stuck on a problem, please just give hints and not full solutions (This is in fact a rule on the Maths forum, so please adhere to it). Little nudges, don't reveal "crux moves". No ruining the fun.

If you have solved a problem and want to have the solution checked on here, please spoiler it. If others are trying to attempt the same problem and they see the solution, then they aren't going to learn anything.
You can spoiler a text by doing this: [*spoiler] YOUR TEXT HERE (Just remove that *)

Tools and Theorems
Note: These theorems aren't necessary for the JMC/IMC/SMCs, nor will they be needed for the IMOK (Circle Theorems are a clear exception), however, they may be of use in BMO1 and most of these will be assumed to be known for the BMO2

Tools and Theorems

Useful Websites

Recommended Books

UKMT Website

http://www.ukmt.org.uk/

British Maths Olympiad Subtrust

http://www.bmoc.maths.org/

(edited 9 years ago)

Scroll to see replies

Reply 1

User990473

Last year I got gold and looking to get a little further this time. I'm hoping I'm a more competent mathematician this year :yep:

(edited 10 years ago)

Reply 2

0x2a

Original post by Occams Chainsaw

Last year I got gold and looking to get a little further this time. I'm hoping I'm a more competent mathematician this year :yep:

Hello!

Try out a few past papers questions, it's the only way to improve :wink:

Reply 3

User990473

Original post by 0x2a

Hello!

Try out a few past papers questions, it's the only way to improve :wink:

Nah. I didn't do any last year and I won't this year. I'm sure completing A Level maths will have improved me enough. I want to see the difference in my ability without looking at papers :naughty:

Reply 4

ryanb97

cool .... this seems good!

Reply 5

0x2a

Original post by Occams Chainsaw

Nah. I didn't do any last year and I won't this year. I'm sure completing A Level maths will have improved me enough. I want to see the difference in my ability without looking at papers :naughty:

Tell me how you do in it. :lol:

Reply 6

0x2a

Original post by ryanb97

cool .... this seems good!

Which one will you be doing this year?

Reply 7

ryanb97

Original post by 0x2a

Which one will you be doing this year?

Senior maths challange.... hopefully will be on the senior maths team as well :biggrin:

yourself ?

Ryan

Reply 8

0x2a

Original post by ryanb97

Senior maths challange.... hopefully will be on the senior maths team as well :biggrin:

yourself ?

Ryan

Senior as well. I have an IMC year left as well (I'm in Year 11).

Reply 9

123formyabc

I skimmed a bronze last year wohoo

Reply 10

ToLiveInADream

Lol, my school force maths top sets into this. I've done it for the past few years, and have gotten silver like twice? I usually spend the hour or so staring at the clock :redface:

Reply 11

suzylemonade

Thanks for this, I am determined to get above a gold this year so hopefully this will help :biggrin:

Reply 12

ChildishHambino

Haha already stuck on the first BMO question round 1 1993. First time at attempting them though.

This is what i've got so far:

Spoiler

Reply 13

0x2a

Original post by ChildishHambino

Haha already stuck on the first BMO question round 1 1993. First time at attempting them though.

This is what i've got so far:

Spoiler

I remember this killing me when I was doing it ages ago.

Spoiler

(edited 10 years ago)

Reply 14

ChildishHambino

Original post by 0x2a

I remember this killing me when I was doing it ages ago.

First represent it like this

N = 1001a + 1 = k^2

Now try and manipulate algebraically. Also representing individual digits isn't a very effective method for this.

Keep going :smile:

Ahh thanks am i along the right lines below?

Spoiler

EDIT: nvm i tried it and it worked woo!! roll on the second question lol

(edited 10 years ago)

Reply 15

0x2a

Original post by ChildishHambino

Ahh thanks am i along the right lines below?

Spoiler

Yup!

You'll get a couple of equations. To solve these a method known as the Extended Euclidean Algorithm might be of use.

Reply 16

ChildishHambino

Original post by 0x2a

Yup!

You'll get a couple of equations in the form

ax - by = 2

. There's a very simple method of solving such linear equations, which is called the Extended Euclidean Algorithm.

You can either use this method (which I can explain to you if you want to) or you can just brute force it.

Would the algorithm find all the solutions much faster i'm guessing?

(edited 10 years ago)

Reply 17

0x2a

Original post by ChildishHambino

Would the algorithm find all the solutions much faster i'm guessing?

Spoiler

I just realised that I wasn't spoiler-ing all the hints, what a hypocrite :facepalm:

(edited 10 years ago)

Reply 18

TheHolubowskyj

I was so miffed when I was one point short of gold last year... really sad I'm not doing it this year to beat my score, but good luck to everyone taking it! :smile:

Reply 19

ChildishHambino

Original post by 0x2a

Spoiler

I just realised that I wasn't spoiler-ing all the hints, what a hypocrite :facepalm:

Ah that's really interesting and haha just realised i didn't for that last post! Anyway i wish that the SMC wasn't a day after the MAT actually wanted to have some practice this year :tongue: