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Home » The possible residues modulo 3 are 0, 1, and 2: - Simpleprint

The possible residues modulo 3 are 0, 1, and 2: - Simpleprint

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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Case 2a: odd non-primes count = 1 → total odd count = 1 (prime) + 1 =...
Case 2b: odd non-primes = 2 → total odd = 1 + 2 = 3 → odd → invalid
Case 2a valid, others invalid
So only 2a: 2 (prime assignments) × 2 (odd non-prime) × 2 (even non-pr...
Plus position arrangement: the even prime and odd prime are in differe...
For Case 2:
Choose 2 positions for the two prime rolls: $ \binom{4}{2} = 6 $
Assign one prime as 2, one as odd (3 or 5): 2 ways (which is which)
Odd prime choice: 2
Non-primes: one must be odd (1), one even (4 or 6): 2 choices

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But the question asks for hours, so final answer is 10,000 × 0.2 × 0.0...
However, the correct calculation is: 10,000 × 0.2 × 10⁻³ = 2 seconds =...
But let's simplify: 500 data points/hour → 10,000 / 500 = 20 hours.
Alternatively, per data point: 0.2 ms = 0.0002 seconds. 10,000 × 0.000...
#### 0.000555
Using direct hours calculation: 10,000 data points × 0.2 ms/data point...
Convert to hours: 2,000 ms = 0.002 seconds = 0.002 / 3600 ≈ 5.555... ×...
But this seems inconsistent. Re-evaluate:
ms per data point = 0.2 × 10⁻³ seconds = 2 × 10⁻⁴ seconds.
Total time: 10,000 × 2 × 10⁻⁴ = 2 seconds.

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