Consider an n x n matrix/grid. Two ants, A and B, are located at opposite corners of the grid (A is at the top-left and B is at the bottom-right). Both ants are trying to meet each other. On each move, ant A can move either one step to the right or one step downward. Similarly, ant B can move one step to the left or one step upward. They can move simultaneously. Given that both ants cannot occupy the same square at the same time (except if they meet), in how many ways can the two ants meet on the grid without crossing each other's path, for n=4?
Consider an n x n matrix/grid. Two ants, A and B, are located at opposite corners of the grid (A is at the top-left and B is at the bottom-right). Both ants are trying to meet each other. On each move, ant A can move either one step to the right or one step downward. Similarly, ant B can move one step to the left or one step upward. They can move simultaneously. Given that both ants cannot occupy the same square at the same time (except if they meet), in how many ways can the two ants meet on the grid without crossing each other's path, for n=4?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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This a challenging problem on combinatorics .
Consider an n x n matrix/grid. Two ants, A and B, are located at opposite corners of the grid (A is at the top-left and B is at the bottom-right). Both ants are trying to meet each other. On each move, ant A can move either one step to the right or one step downward. Similarly, ant B can move one step to the left or one step upward. They can move simultaneously.
Given that both ants cannot occupy the same square at the same time (except if they meet), in how many ways can the two ants meet on the grid without crossing each other's path, for n=4?
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