The September Problems are here!
Wednesday, August 26, 2009 16:27Well, it may not attract the same amount of press that the arrival of the Beaujolais Nouveau does, but this year’s September problems which we use to select students to attend camp in January are now available.
Please read the instructions and registration document carefully (.doc version). In particular, note that you are to spend at most 10 days working on the problems, and not to get outside aid of any sort (including, it should be needless to say, from the internet).
Please note also that these problems are not a competition in the ordinary sense of the word. We use them simply as a filter to determine the 24 students to invite to camp. In particular, within that 24 or outside that 24 we don’t rank the outcomes.
Finally, good luck with the problems!
HOANG QUOC VIET says:
September 2nd, 2009 at 5:58 pm
I want to take part in the training for IMO team with the specific field of Inequality. How can I apply for that position? I am the first year student of Auckland University and ambitious to gain more experience since I want to be a teacher in the future.
Arthur says:
September 29th, 2009 at 12:08 am
I don’t understand what question 3 is asking.
3. Let A be a subset of {1, 2, 3,…, 2010} having the property that the difference of any two elements of A is not a prime number. What is the largest possible number of elements of A? (Note, 1 is not a prime number).
Would an example is 1 and 8? Or would that be two examples? Is that an element of A? so then the answer would be huge right? like millions or something?
Michael says:
September 29th, 2009 at 6:53 am
The question is simply how many elements can a subset of {1,2,3,…,2010} have if it has the additional property that if you take any two elements in the subset their difference is not prime.
To put it in greedy terms: if I were to offer you $1 per element in such a subset, what’s the maximum amount of money you could collect from me? [I hasten to add that I am not, in fact, making such an offer!]
animesh says:
October 21st, 2009 at 12:58 am
So what is the answer to this question and how do you reach that answer?
Let A be a subset of {1, 2, 3,…, 2010} having the property that the difference of any two elements of A is not a prime number. What is the largest possible number of elements of A? (Note, 1 is not a prime number).
Michael says:
October 21st, 2009 at 6:57 am
As Chris mentioned, there’s been a de facto extension of the submission deadline, so it’s a bit early to be providing answers! Sorry, you’ll have to contain your excitement for another couple of weeks.
Yldolce says:
October 24th, 2009 at 8:16 pm
Ugh… so all the answers will be here when the deadline is in?
please give the answers… I am desperate!
Jessy says:
October 31st, 2009 at 10:26 am
Can I know the answer to question number three now? It’s past the deadline! stuck on it for hours!
Michael says:
November 3rd, 2009 at 8:10 am
Solutions have now been posted.