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How many 5 block paths can take you home if walking 2 blocks north then 3 blocks west got you here? This should feel familiar if you're from NYC, Chicago, Barcelona, or Toronto!

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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?

12 16 27 24

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by Chung Kevin

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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.

\[ { 5 \choose 2 } \times { 5 \choose 2 } \] \[ { 5 \choose 2 } \times { 4 \choose 2 } \] \[ { 4 \choose 2 } \times { 4 \choose 2 } \] \[ { 4 \choose 2} \times { 4 \choose 1 } \]

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by Chung Kevin

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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?

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by Chung Kevin

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

3360 440 100 20

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by tanay gaurav

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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?

\[ { 3 \choose 2 } { 6 \choose 1 } \] \[ 126 - { 3 \choose 2 } { 6 \choose 1} \] \[ { 3 \choose 1 } { 6 \choose 2 } \] \[ 126 - { 3 \choose 1 } { 6 \choose 2 } \]

Excel in math and science

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by Chung Kevin

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Cancel Yes I'm sure

Waste less time on Facebook — follow Brilliant.

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations, examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

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Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations, examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Concept Quizzes

Challenge Quizzes

Rectangular Grid Walk: Level 2 Challenges

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations, examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations, examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations, examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations, examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations, examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Master advanced concepts through explanations,
examples, and problems from the community.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Master advanced concepts through explanations,
examples, and problems from the community.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Master advanced concepts through explanations,
examples, and problems from the community.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Master advanced concepts through explanations,
examples, and problems from the community.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Master advanced concepts through explanations,
examples, and problems from the community.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Master advanced concepts through explanations,
examples, and problems from the community.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Master advanced concepts through explanations,
examples, and problems from the community.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.