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Home » Unlock Your Grit: Powerful Motivational Sports Quotes That Will Ignite Your Drive - Crankk.io

Unlock Your Grit: Powerful Motivational Sports Quotes That Will Ignite Your Drive - Crankk.io

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 Next, compute the number of paths that pass through the forbidden square at (3,3). To do this, split the path into two parts: from (1,1) to (3,3), and from (3,3) to (5,5).

📌 From (1,1) to (3,3): 2 R and 2 U moves → $\binom{4}{2} = 6$

📌 From (3,3) to (5,5): 2 R and 2 U moves → $\binom{4}{2} = 6$

📌 So, number of paths through (3,3) is:

📌 Thus, the number of valid paths avoiding (3,3) is:

📌 - 36 = \boxed{216}

📌 Question: A hydrologist is modeling water flow through 6 distinct layers of soil, each with unique permeability. In how many ways can the layers be arranged vertically so that the most permeable layer is not directly above the least permeable layer?

📌 Solution: First, compute total number of permutations of the 6 distinct layers:

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