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Home » Number of ways: \(\binom63 = 20\) - Simpleprint

Number of ways: \(\binom63 = 20\) - Simpleprint

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 Solution: A regular octahedron has 8 equilateral triangular faces. The area of one face is $\frac{\sqrt{3}}{4} \times 4^2 = 4\sqrt{3}$. Total surface area: $8 \times 4\sqrt{3} = 32\sqrt{3}$ nm².

📌 \boxed{32\sqrt{3}}Question: What is the largest possible number of identical research grants that can be awarded using 2025 and 1515 units of funding, ensuring no funds remain unallocated?

📌 Solution: To determine the largest number of identical grants, compute $\gcd(2025, 1515)$.

📌 Factorize:

📌 $2025 = 3^4 \times 5^2$

📌 $1515 = 3 \times 5 \times 101$

📌 The $\gcd$ is the product of the smallest powers of common primes: $3^1 \times 5^1 = 15$.

📌 Thus, the maximum number of grants is $\boxed{15}$.

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