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ask and ye shall receive - Midis

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 The LCM takes the highest power of each prime: $2^3$ and $3$.

📌 So, $ ext{LCM} = 2^3 \cdot 3 = 8 \cdot 3 = 24$.

📌 Therefore, all three fields will be sampled on the same day again in $oxed{24}$ days.

📌 Question: An epidemiologist models the spread of a virus where each infected person infects 3 others in a geometric progression. If the initial number of infected individuals is 1, how many total individuals have been infected by the end of the 5th generation?

📌 Solution: This is a geometric sequence with first term $a = 1$ and common ratio $r = 3$. The total number infected by the end of the 5th generation is the sum of the first 5 terms:

📌 S_5 = a \cdot rac{r^5 - 1}{r - 1} = 1 \cdot rac{3^5 - 1}{3 - 1} = rac{243 - 1}{2} = rac{242}{2} = 121.

📌 Thus, the total number of individuals infected is $oxed{121}$.

📌 Question: In a VR puzzle, a player must guess a 3-digit code where each digit is a factor of 24. How many valid codes are possible?

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