You start in the top left corner of a 6x6 grid. Your goal is to get to the bottom right corner. You can only move to the right or down. You can't move diagonally and you can't move backwards.

How many different ways are there to get from the start to the finish?

For example, all the paths below, starting with S in the upper left corner, are possible.

If there are 9 ways of getting to the square to the left, and 5 ways of getting to the square above how many way are there of getting to the square with the question mark?

You may also want to refresh your memory on Pascal's Triangle.

Take a moment to think about why, it can take a moment. Remember we are not counting the moves, but the possible combinations of different moves.

From here it's not that difficult to fill in the grid with the number of possible combinations of moves to reach each square. We know that there is only one way of reaching any square in the top row, and similarly there is only one way of reaching every square in the left hand column. Then just fill in the numbers...

So there are 252 different ways the traveler can get from the top left corner to the bottom right corner.

What if the grid were 7 by 7? In how many different ways could one travel from the upper left corner to the bottom right corner?

This problem can be found at http://puzzles.nigelcoldwell.co.uk/seventyone.htm