দৈনন্দিন জীবনে বস্তু গোনবার পদ্ধতি খুব কাজের জিনিস । এই পোস্ট থেকে একটি পদ্ধতি সম্বন্ধে জানব যা ডিরিশিলিটের বাক্স নীতি বা ইংরেজিতে Pigeonhole principle বলে।
দৈনন্দিন জীবনে বস্তু গোনবার পদ্ধতি খুব কাজের জিনিস । এই পোস্ট থেকে একটি পদ্ধতি সম্বন্ধে জানব যা ডিরিশিলিটের বাক্স নীতি বা ইংরেজিতে Pigeonhole principle বলে।
This post contains RMO 2007 problems. Try to solve these problems Let ABC be an acute-angled triangle; AD be the bisector of angle BAC with D on BC, and BE be the altitude from B on AC. Show that $ \angle CED > 45^\circ $ . [weightage 17/100] Let a, b, c be three natural […]
Let's understand the factor method of Diophantine equations step-by-step. Aso, try the question related to it. Diophantine Equations Consider an equation for which we seek only integer solutions. There is no standard technique of solving such a problem, though there are some common heuristics that you may apply. A simple example is $ x^2 - […]
Here is an excerpt from an email conversation that I had with one of our student's parent: "While we have lots of books with problems, the one challenge has been that problems in the books are not classified by level of difficulty or arranged in increasing order of difficulty. Much like a weight-lifter gradually increases […]
This is a session plan for 'Mathematics in Summer 2014'. (Venue: Scotland, Glasgow). Let's discuss Homological Triangles. Introduction to homological triangles, perspectivities. Menalaus' Theorem, Desargues Theorem Anti parallel lines, some examples of homological triangles, homothety as a special case of homology, cevian, orthic triangle, some basic properties of angle bisectors' Special Triangles and points: anti-supplemental […]
A post on homological triangles... topic of our math camp August 2014 (in Scotland)
a and b are two numbers having the same no. of digits and same sum of digits (=28). Can one be a multiple of the other? a is not equal to b. (courtesy Abhra Abir Kundu) Is $latex e^x-sinx $ a polynomial ? (courtesy Tias Kundu) Find the number of onto function from set A containing […]
This post contains an interesting problem from ISI BMath 2014 based on the jump of a frog and the lotus. Solve and enjoy this problem. Problem: Jump of a frog Problem n (> 1) lotus leafs are arranged in a circle. A frog jumps from a particular leaf by the following rule: It always moves […]
This is a problem from CMI Entrance 2014 based on Map from a power set to n-set. Problem: Map from a power set to n-set (1) Let A = {1, ... , k} and B = {1, ... , n}. Find the number of maps from A to B . (2) Define $latex \mathbf{ P_k […]