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Home » Lösung: Sei \(p\) die Anzahl der Projekte, die Liam benötigt. - Network4

Lösung: Sei \(p\) die Anzahl der Projekte, die Liam benötigt. - Network4

📅 May 19, 2026 👤 scraface

May 19, 2026

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📌 Question: A community garden coordinator in Brooklyn is planning a layout where plots are labeled in base 7. If a plot is labeled $ 314_7 $, what is its label in base 10?

📌 Solution: Convert $ 314_7 $ to base 10:

📌 314_7 = 3 \cdot 7^2 + 1 \cdot 7^1 + 4 \cdot 7^0 = 3 \cdot 49 + 1 \cdot 7 + 4 = 147 + 7 + 4 = 158

📌 \boxed{158}

📌 Question: What is the remainder when $ 2023 + 2025 + 2027 + 2029 $ is divided by 8?

📌 + 2025 + 2027 + 2029 = (2023 + 2029) + (2025 + 2027) = 4052 + 4052 = 8104

📌 Now compute $ 8104 \mod 8 $. Since 8100 is divisible by 8 (as $ 8100 \div 8 = 1012.5 $, but $ 8000 \div 8 = 1000 $, and $ 100 \div 8 = 12.5 $), we check only the last three digits:

📌 \div 8 = 13 \text{ exactly}, so } 8104 \equiv 0 \pmod{8}

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