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# More problems (competition) watch

1. All answers must be in PMs to me, and they must be your own. There will be 12 questions across a large range of difficulties. Each correct answer is awarded 1 point, a suitable explanation is awarded 1 more point. 1 extra point awarded for clarity... no writing things like 2^2x-1 please, if your keyboard has brackets please use them. This gives 25 points which can be scaled up to a percentage easily.

I will post the problems in about 15 minutes in a seperate thread and ask that no one posts answers there... If they do it will ruin the whole thing. Perhaps a mod could close it.

I may run a scoreboard if people don't mind ... if you DO mind, then please say explicitly in the PM with your answers. If you don't, I may or may not depending on time and how many others mind.

Scores will be PM'd in a reply 2 weeks from now. I don't know how many replies this will generate and it is not fair to exclude people who miss this thread, so at the moment I am planning to take answers until 10 days from this time roughly. No immediate hurry, although some problems will be challenging.

Good luck.

Any questions?
2. can we use the calculator?? brilliant idea though
3. can we use the calculator??

brilliant idea though well done
4. (Original post by integral_neo)
can we use the calculator?? brilliant idea though
Only to do work that will make your life easier. To find 622215/11, yes, as you could use long division. To find the 1000s digit in 7^55, no. And bear this in mind when writing explanations.
5. sounds a good idea... i'm game!
6. Hmmm what if we already know some equalities from other situations ( eg: if I know how to express 1/2 + 1/8 + etc...); should we then explain them also?
7. (Original post by Wagamuffin)
Hmmm what if we already know some equalities from other situations ( eg: if I know how to express 1/2 + 1/8 + etc...); should we then explain them also?
Yes.
8. mik1a, can you explain question 12? surely the sum of k consecutive positive integers to total 3^11 can only have only one value of k? what do you mean to find the largest value?
9. (Original post by 4Ed)
mik1a, can you explain question 12? surely the sum of k consecutive positive integers to total 3^11 can only have only one value of k? what do you mean to find the largest value?
2+3+4 = 4+5 = 9

Here k = 3, 2 and 1 respectively.

The question, if applied to the number 9, would be k = 3.
10. (Original post by mik1a)
2+3+4 = 4+5 = 9

Here k = 3, 2 and 1 respectively.

The question, if applied to the number 9, would be k = 3.

mik1a please check i think question 4 has a flaw.
11. I only seem to be able to do some of the easy ones and one of the medium ones....
What Level are these questions based upon????
plz rememba I just finished my GCSE's
plz dnt say I should be able to do this!!!
and there was me thinkin I was an A grade kid in GCSE
DAAAAAAAAAAMMMMNNNNNNNN!!!
12. (Original post by Fade Into Black)
I only seem to be able to do some of the easy ones and one of the medium ones....
What Level are these questions based upon????
plz rememba I just finished my GCSE's
plz dnt say I should be able to do this!!!
and there was me thinkin I was an A grade kid in GCSE
DAAAAAAAAAAMMMMNNNNNNNN!!!

I would say that these questions are aimed at A-levels students ( yes i mean all of them including easy ones) so if u have managed to do any of them u should be pleased with yourself!

the only questions qhich i think can de done without any a-level knowledge are: (2), (3) and may be (7) and (8) but still if a GCSE student does any of them he would have to be quite bright in my opinion
13. (Original post by integral_neo)
mik1a please check i think question 4 has a flaw.
Is that the one with,
12!/n! = 11880 ?
I've done that one it it comes out ok.
14. I've done all the questions, but I've written the solutions up in latex and they're now in a pdf file. I don't think I can send attachments by pm. Would it be alright to email them??
15. could someone please explain to me the concept of number bases, so that i could have a go at question nine? if you could start from the basics that would be v. much appreciated.

Tatum
16. (Original post by Drederick Tatum)
could someone please explain to me the concept of number bases, so that i could have a go at question nine? if you could start from the basics that would be v. much appreciated.

Tatum
basically, we tend to count in base 10 (1,2,3,4,5,6,7,8,9,10...). In this system of counting, each number will have a value for units, 10s, 100,s etc, so like for 876 you have units=6, 7 10s, and 8 100s (this was probably taught in year 5 and will seem very obvious). Anyway, if say you were counting in base 9, then rather than there being 10s you would have 9s and rather than 100s you would have 9^2, or 81, etc so counting would proceed 1,2,3,4,5,6,7,8,10,11,12,13,14,1 5,16,17,18,20,21........ and clearly the number after 88 is 100, etc. Counting in base 4 is just 1,2,3,10,11,12,13,20,21,22,23,..
17. ta very much

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