Bose Olympiad Senior is suitable for kids in Grade 8 and above. There are two levels of this olympiad:
The following topics in number theory are useful for the Senior round:
Here is an example of a Number Theory problem that may appear in Seinor Bose Olympiad:
Suppose $a, b, c$ are the side lengths of an integer sided right-angled triangle such that $GCD(a, b, c) = 1$. If $c$ is the length of the hypotenuse, then what is the largest value of the $GCD (b, c)$?
Key idea: Pythagorean Triples
The following topics in geometry are useful for the Senior Bose Olympiad round:
Here is an example of a geometry problem that may appear in the Senior Bose Olympiad:
Suppose the river Basumoti is 25 meters wide and its banks are parallel straight lines. Sudip's house 10 meters away from the bank of Basumoti. Apu's house is on the other side of the river, 15 meter away from the bank. If you are allowed to construct a bridge perpendicular to the banks of Basumoti, what is the shortest distance from Sudip to Apu's house.
Key idea: Reflection
The following topics in Algebra are useful for Intermediate Bose Olympiad:
Here is an example of an algebra problem that may appear in Senior Bose Olympiad:
The following sum is greater than which integer: $$ \frac{2}{3} + \frac{3}{4} \cdots + \frac{2019}{2020} + \frac{2020}{2} $$
(A) $2019$ (B) $2020$ (C) $2021$ (D) $2022$
Key idea: inequality
