Блог пользователя MikeMirzayanov

Автор MikeMirzayanov, 6 лет назад, По-английски

Many thanks to problem authors — Tech Scouts instructors. Please, review the author's solutions. They are beautiful and short. Our community has many to learn from mathematicians!

Tutorial is loading...
Tutorial is loading...
Tutorial is loading...
Tutorial is loading...
Tutorial is loading...
Tutorial is loading...
Tutorial is loading...
Tutorial is loading...
Tutorial is loading...
Tutorial is loading...
Tutorial is loading...
Tutorial is loading...
Tutorial is loading...
Tutorial is loading...
Tutorial is loading...
Tutorial is loading...
Tutorial is loading...
Tutorial is loading...
Tutorial is loading...
Tutorial is loading...
Tutorial is loading...
  • Проголосовать: нравится
  • +49
  • Проголосовать: не нравится

»
6 лет назад, # |
  Проголосовать: нравится +68 Проголосовать: не нравится

To me, the answer for K seems ambiguous as there can be considered to be 2018 sequences covering the whole circle. Hence, 2018*2019/2 is the answer that I was getting (even though I did not participate).

»
6 лет назад, # |
  Проголосовать: нравится 0 Проголосовать: не нравится

»
6 лет назад, # |
  Проголосовать: нравится 0 Проголосовать: не нравится

1164R — Divisible by 83 , Anser is 0, 0 mod 83 = ???? :)))

»
6 лет назад, # |
Rev. 2   Проголосовать: нравится +29 Проголосовать: не нравится

I think the answer to problem K should be $$$\frac{2018*2017}{2}+2018=2037171$$$
The whole circle may be counted 2018 times (because a sequence is an enumerated collection of numbers and there are 2018 possible starting points)
It can be seen that these 2018 sequences are pairwise distinct.

»
6 лет назад, # |
  Проголосовать: нравится +1 Проголосовать: не нравится

Why areas are 3 in B? I used affine transformations in B, to solve

  • »
    »
    6 лет назад, # ^ |
      Проголосовать: нравится +3 Проголосовать: не нравится

    The area of triangle ABP will be equal to 3/(1+3) of the area of the triangle ABC as P divides AC as 3:1. The area of triangle AMP will be equal to 1/(1+3) of the area of the triangle ABP as M divides AB as 1:3. Therfore, area of triangle AMP will be equal to 3/4 * 1/4 = 3/16 of the area of ABC.

»
6 лет назад, # |
  Проголосовать: нравится +8 Проголосовать: не нравится

Well, I for got the +1 in Problem K :'(

»
6 лет назад, # |
  Проголосовать: нравится +18 Проголосовать: не нравится

Is there a way to submit my answers now ? I couldn't take part of the contest and I would like to submit it ... Thanks :3

»
6 лет назад, # |
  Проголосовать: нравится +2 Проголосовать: не нравится

In some of these problems, you could take one particular instance and work out the answer for that, since you know there is only 1 answer to the problem (because of how the system works).

For example, for the 2018 integers written on a circle with sum 1. You can assume 2017 of them are positive and one of them is the negative sum of all the others +1. It's now easy to see that all sequences that do not contain the negative number are positive.

»
5 лет назад, # |
  Проголосовать: нравится 0 Проголосовать: не нравится

Can any one elaborate the solution of problem 1164I — maximum value please . How to transform the equality (a+b−1)2=ab+1 to obtain a2+b2=4−(a+b−2)2≤4 ??

»
4 года назад, # |
Rev. 2   Проголосовать: нравится 0 Проголосовать: не нравится

Please make another mathforces contest.