Editorial of Calibration Round #31

Problems link: Problems | Calibration Round #31 | গণিতযজ্ঞ

Problem A. সম্ভাব্য উপায়গুলি

  1. Consider Parthib and Abdur Rahman as the same letter a of a string.
  2. Let the string be aabcdef.
  3. Now count its permutation.

Problem B. লম্বকোণ
There was some error in the statement. Why don’t you try to answer a question "A triangle ABC has an obtuse angle at B. The perpendicular at B to AB meets AC at D, and CD=AB.
Prove that AD^2=AB×BC if and only if \angle CBD=30° ". Can it be proved? Or what might be the error?

Problem C. বৃহত্তম বিভাজক
Find parity and try to use modular arithmetic.

Problem D. গোলীয় ক্ষেত্র মধ্যবৃত্ত
Let G be the centroid of ABC. By using Heron’s formula, find the area of AFG and do the rest at your own risk.

Problem E. মধ্যমার প্যাঁচ
Let G be the centroid and we have AB^2=AG^2+BG^2.

Problem F. শখে গড়া সেট
The number are from fibonacci series and they are from both positive and negative side.


When will the upsolve on ?