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Home » This Trickster Bridge Will Change How You See Hidden Paths Forever! - Sourci

This Trickster Bridge Will Change How You See Hidden Paths Forever! - Sourci

📅 May 1, 2026 👤 scraface

May 01, 2026

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📌 Question: What is the greatest common divisor of 2025 and 1024?

📌 Solution: The prime factorization of 2025 is $3^4 imes 5^2$, and 1024 is $2^{10}$. Since there are no common prime factors, the GCD is 1. The answer is $oxed{1}$.

📌 Question: What is the remainder when $1^2 + 2^2 + \cdots + 15^2$ is divided by 13?

📌 Solution: The sum of squares formula gives $S = rac{15 imes 16 imes 31}{6} = 1240$. Compute $1240 \mod 13$: $13 imes 95 = 1235$, so $1240 - 1235 = 5$. The remainder is $oxed{5}$.Question: A science educator is designing a lesson on probability using a digital simulation that generates random 6-digit numbers using only the digits 1, 2, and 3. What is the probability that a randomly generated number has exactly two consecutive digits that are the same?

📌 Solution: To solve this, we must count the number of 6-digit numbers using only the digits 1, 2, and 3 such that exactly one pair of consecutive digits are equal, and all other adjacent digits are different.

📌 Letâs denote the digits of the number as $ d_1, d_2, d_3, d_4, d_5, d_6 $, where each $ d_i \in \{1, 2, 3\} $.

📌 ### Step 1: Total number of 6-digit numbers using digits 1, 2, and 3

📌 Each digit has 3 choices, so the total number of such numbers is:

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