You have a 6 x 6 grid. You start at the top left corner and your "finish square" is the bottom right corner. You can only move to the right or move down. How many ways are there for you to get to the "finish square"?
closed as off-topic by Emrakul♦ Mar 30 at 3:33
This question appears to be off-topic. The users who voted to close gave this specific reason:
Assuming that each "movement" moves me exactly one grid square, there are
Alternative way of solving (that arrives at the same solution).
Since this puzzle is tagged "Visual" and not "Math," I'll provide a more visual solution as well. We will find how many paths there are from each square. The number of paths from the initial square is, of course, the solution.
To begin with, there is exactly one path from the goal to the goal (namely: you're already there!). Additionally, if you are already in the final row or column, there is only one path to the goal (follow that row or column to the end).
Our table so far looks like this:
Then, observe that for each of those question marks, since we can choose to move to either the space below us or to the right, each space has a number of paths equal to the sum of its two reachable neighbors. We can start by filling in a "2" in the one space whose neighbors we both know, and then work row by row and column by column.