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Home » Thus, number of non-adjacent triplets is 16. - Abbey Badges

Thus, number of non-adjacent triplets is 16. - Abbey Badges

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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But $I$ must be an integer, and $9\sqrt{3} \approx 9 \cdot 1.732 = 15....
Instead, interpret the problem as a combinatorial lattice: suppose the...
From combinatorial geometry, the number of lattice points strictly ins...
Number of interior points (in unit triangular lattice): $ \frac{(n-2)(...
Alternatively, for a large equilateral triangle of side $n$ in a trian...
I = \frac{(n-1)(n-2)}{2}
For $n = 6$:
I = \frac{(6-1)(6-2)}{2} = \frac{5 \cdot 4}{2} = 10
This formula arises from known results in triangular lattice geometry:...
Thus, the number of interior lattice points is $ \boxed{10} $.Question...

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Now check divisibility: \( 2025 \div 3 = 675 \), remainder 0. Thus:
\gcd(2025, 3) = 3
Hence, the greatest common divisor is \(oxed{3}\).
A community nutrition educator is organizing a cooking workshop. If th...
Let \( d = \gcd(p, q) \). Then \( p = dk \), \( q = dl \) with \(\gcd(...
dk + dl = 150 \implies d(k + l) = 150
To maximize \( d \), minimize \( k + l \). Since \(\gcd(k, l) = 1\), t...
d imes 2 = 150 \implies d = 75
Since 75 divides 150 and \( k + l = 2 \) satisfies coprimality, the la...
An entomologist is examining the cycles of a rare insect species, wher...

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