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STEP Support Programme

a small problem---- the image

I am a student from China, as I solving the problem on the basic module, assignment 11, I had a little problem with the first question. the answer says we need to show this question with the billiard ball. can anyone show me an image about it (I guess it may be the image of the sum of arithmetic sequence on the book)
thanks a lot

Can you link the assignment? I have had a look at assignment 11 and I cannot find a billiard ball in there.

Or you can type out the question?

thank you for your help, just the answer of the 1 (i)
https://maths.org/step/sites/maths.org.step/files/Feedback_A11_1.pdf [this is the link]

This does NOT say you NEED to prove anything with billiard balls. It just notes that if you arrange balls into an equilateral triangle of size $n$, then $T(n)$ will be the total number of balls used. But that's of no real importance to the question.

The billiard balls are not important (as has been said above). It was meant to try and provide a mental image for people - such as the one on this page.

thank you for your information,

In addition, if I want to attend STEP I, II and III at the end of year 12 (I'm year 11 now), should I finish these 3 STEP modules during the summer holidays?

best wishes,
Kervin Liu

I would concentrate on the Foundation modules for this summer, moving onto the STEP 2 and STEP 3 modules after the summer.

thanks a lot, so should I go through the past papers during the next years.

inaddition, during go through british maths olympiad round 1 question (although i heard maybe i'm not allowed to attend it), I find combinatorics a really challenge part, should I carry on solving combinatorics or should I going on learning number theory (which seems the part I 'm interested in recently´╝ë

thanks

It depends on what your goals are. For BMO Round 1, the number theory that comes up is usually just simple modulo arithmetic and easy (factorisable) integer equations. But combinatorial-type problems do come up a fair bit, because they don't require much advanced theory/knowledge, so these problems can be asked on an introductory Olympiad like BMO Round 1. For university, you probably won't study number theory or combinatorics specifically until you get to choosing options in your third year.