How to Calculate Shortest Paths in a Grid

TL;DR

To calculate the number of different shortest paths in a rectangular grid, you can use combinations. If there are 5 columns and 4 rows, Zara can take 126 distinct paths by selecting 5 moves to the right out of a total of 9 moves, represented mathematically as '9 C 5'. Alternatively, this can be viewed as arranging 5 'R's and 4 'U's.

Transcript

We have been given this rectangular grid of paths with this being the starting point and this being the destination. Zara's at the starting point and wants to reach the cake shop which is at the destination. Think of these lines as paths Zara can take to travel to the cake shop. With this, we have been asked for the number of different shortest pat... Read More

Key Insights

• 🍰 The problem involves finding the number of different shortest paths in a rectangular grid.
• 🫱 Shortest paths only involve moving rightwards or upwards.
• 💌 Both combinations and arranging letters can be used to calculate the number of shortest paths.
• 🤨 The number of columns and rows in the grid determines the total units traveled.

Questions & Answers

Q: How do we define a shortest path in the given problem?

In this problem, a shortest path consists of moving only rightwards or upwards in the rectangular grid.

Q: What is not considered a shortest path?

A path that involves moving leftwards or downwards at any point is not considered a shortest path.

Q: How can we calculate the number of shortest paths using combinations?

By using the formula for combinations, specifically "NCR," where N represents the total units traveled and R represents the number of units moved rightwards or upwards.

Q: Are there alternative methods to calculate the number of shortest paths?

Yes, arranging the letters "R" (for right) and "U" (for upwards) in all possible combinations can also give the number of different shortest paths.

Summary & Key Takeaways

• The problem involves finding the number of different shortest paths a person can take in a rectangular grid to reach their destination.

• The shortest path consists of moving only upwards or rightwards.

• The number of shortest paths can be calculated using combinations or arranging letters in a word.