Probability

# Rectangular Grid Walk: Level 2 Challenges

Anna and Ben live at opposite corners of a 3 by 4 block.
If Anna only moves right or up or down, and isn't allowed to retrace her steps, how many ways does she have to get to Ben?

I was on vacation in England, and wanted to visit the Tower of London. The roads were laid out on a grid map, and and the castle was 4 blocks north and 5 blocks east. I also wanted to visit the Apple store along the way, and check out the new IWatch.

If I were to travel only north and east, how many routes did I have to get to the castle?

See Part 1, Part 2, Part 4, and Part 5.

I was on vacation in England, and wanted to visit the Tower of London. The roads were laid out on a grid map, and and the castle was 4 blocks north and 5 blocks east. I also want to get at least one ice cream cone along the way. I knew that there were 2 ice cream shops that I could use, and they were conveniently located at an intersection.

If I were to travel only north and east, how many routes did I have to get to the castle?

How many distinct paths consisting of steps only right or down are possible from $P$ to $Q$?

I was on vacation in England, and wanted to visit the Tower of London. The roads were laid out on a grid map, and and the castle was 4 blocks north and 5 blocks east. Unfortunately, there was some police activity near the hotel, and that intersection was blocked off so I could not go through it.

If I were to travel only north and east, how many routes did I have to get to the castle?

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