Problems link: Problems | Calibration Round #21 | গণিতযজ্ঞ

**Problem A. বহুপদীর বিভাজ্যতা**

Divide a^3+a^2+a+1 into two factors. The rest you can understand easily.

**Problem B. বৃত্ত-ত্রিভুজ সংঘর্ষ**

- Just to use the Power of point theorem and easy trigonometric approach.
- Prove that, \triangle NPQ \sim \triangle NOM.

**Problem C. বহিরাগত গুণক**

i) Use AM-GM inequality.

ii) You might find terms like (x-y), (y-z) and (z-x) while manipulating expressions. And you need to use xy+yz+zx often in expansions. So think about it a bit.

**Problem D. ভাগশেষ নির্ণয়**

- Try to express numbers in base 7.
- You can think of it in terms of expansion of (1+x). Then apply combinatorial logic in terms of the power of x.

**Problem E. ভয়কে করো জয়!**

- It has something to do with the power of 2.
- The maximum value is of the form 1- \frac {1}{2^k}.

Find k by yourselves.

**Problem F. দুই ত্রিভুজ**

An easy trigonometric approach using Cosine law. You can use Stewart’s theorem also.