This is a Geometry theorem based on Angles adding up to 180 degrees. It is helpful for Mathematics Olympiad. Try to prove the statement! Statement: Angles adding up to 180 degrees ABC be an isosceles triangle with AB = AC. P be a point inside the triangle such that, $ \angle ABP = \angle BCP […]
Every subgroup of order 74 in a group of order 148 is normal Discussion: True We will prove a much general claim: if index of a subgroup is 2, then that subgroup must be normal. Suppose $ H \le G $ and $ [G:H] = 2$ . Now, if $ g \in H $ then […]
This is an (ever-growing and ever-changing) list of books, useful for school and college mathematics students. If you are working toward Math Olympiad, I.S.I., C.M.I. entrance programs or intense college mathematics, these books may prove to be your best friend. If you are taking a Cheenta Advanced Math Program, chances are that you will referred […]
Let's discuss this objective problem number 14 from ISI BStat BMath. Try to solve the problem and then read their solution. Problem 14 f(x) = tan(sinx) (x > 0) To understand the graph of a function, easiest and the most proper method is to apply techniques from calculus. We will quickly compute, derivative and second […]
This post contains the six Indian National Maths Olympiad, INMO 2015 problems. Try to solve these problems. Let ABC be a right-angled triangle with $ \angle{B}=90^{\circ} $. Let BD is the altitude from B on AC. Let P, Q and Ibe the incenters of triangles ABD, CBD, and ABC respectively. Show that circumcenter of triangle […]
Let's have a problem discussion of Geometry problems in AIME. (American Invitational Mathematics Competitions). Give them a try. In $ \Delta ABC, AB = 3, BC = 4 $, and CA = 5. Circle $ \omega $ intersects $ \overline{AB} at E and B, \overline{BC} $ at B and D, and $ \overline{AC} $ at […]
Here is a very interesting problem based on counterfeit coin. There are five coins three of them are good one of them is heavier and one of them is lighter. It is not given whether the amount of extra weight in the heavier coin is the same as the amount of lost weight in the […]
Let's try to find the solution to Duke Math Meet 2008 Problem 8. This question is from the individual round of that meet. Problem: Duke Math Meet 2008 Problem 8 Find the last two digits of $ \sum_{k=1}^{2008} k {{2008}\choose{k}} $ Discussion: $ (1+x)^n = \sum_{k=0}^{n} {{n}\choose{k}}x^k $ We differentiate both sides to have $ […]
Try this Remainder problem from Duke Math Meet 2009 Problem 9. This problem is from the Team Round of the meet. Problem: Duke Math Meet 2009 Problem 9 What is the remainder when $ 5^{5^{5^5}} $ is divided by 13 ? By Fermat's Little Theorem $ 5^{12} = 1 \mod 13 $ Now if we […]
Try this problem from Duke Math Meet 2009 Problem 7 based on the number of ordered triples. This problem was asked in the team round. How many ordered triples of integers (a, b, c) are there such that $ 1 \le a, b, c \le 70 $ and $ a^2 + b^2 + c^2 $ […]