This is an optional module for those appearing only for the Engineering exams. Practice Problems Q-1) Find the number of 2 digit positive integers that are divisible by both of their digits. Q-2) How many ways are there to arrange the numbers 1,2,3…,64 on a 8×8 chessboard such that the numbers in each row and… Continue reading
Category: Combinatorics
Week -13 | Combinatorics – 9
In this module, we’d discuss a couple of counting strategies that maybe useful while solving problems related to the Olympiads. We’d illustrate these strategies with the help of examples. Ex-1) Let be integers greater than 1. Consider to be a set with elements, and let be subsets of . Assume that for any 2 elements , there… Continue reading
Week -13 | Combinatorics – 8
Practice Problems Q-1) There are p intermediate stations on a railway line between 2 points A and B. In how many ways can a train stop at 3 of the stations such that no 2 of the stopping stations are consecutive? Q-2) How many different numbers smaller than can be formed by the digits 0,1,2… Continue reading
Week – 12 | Combinatorics – 7
This is an optional module for students preparing for the engineering entrance exams. Q-1) Among 6 persons in a room, there are either 3 who know each other or 3 who are complete strangers Solution : Let us consider a hexagon with each person denoting a specific vertex of the hexagon. We join 2 vertices… Continue reading
Week – 12 | Combinatorics – 6
Q-1) Find the number of triangles whose angular points are at the angular points of a given polygon of n sides, but none of whose sides are on the sides of the given polygon. Solution: The polygon has n sides – hence n angular points. We can choose a triangle from these n angular points… Continue reading