1. **Problem Statement:** Majed starts with 2 magic stones. Each time he rubs the stones, every stone produces one new stone. We need to find how many times he must rub the stones to have a total of 100 stones. 2. **Understanding the process:** Initially, Majed has 2 stones. After 1 rub, each stone produces 1 new stone, so the number of stones doubles. This means the number of stones after $n$ rubs is given by the formula: $$ S_n = 2 \times 2^n = 2^{n+1} $$ where $S_n$ is the number of stones after $n$ rubs. 3. **Set up the equation:** We want $S_n = 100$, so: $$ 2^{n+1} = 100 $$ 4. **Solve for $n$:** Take the logarithm base 2 of both sides: $$ n+1 = \log_2 100 $$ Calculate $\log_2 100$: $$ \log_2 100 = \frac{\log_{10} 100}{\log_{10} 2} = \frac{2}{0.3010} \approx 6.644 $$ So, $$ n + 1 = 6.644 \implies n = 5.644 $$ 5. **Interpretation:** Since $n$ must be an integer (number of times rubbed), and $n=5.644$ is not an integer, we round up to the next whole number: $$ n = 6 $$ 6. **Verification:** After 6 rubs, $$ S_6 = 2^{6+1} = 2^7 = 128 $$ which is more than 100 stones. After 5 rubs, $$ S_5 = 2^{5+1} = 2^6 = 64 $$ which is less than 100 stones. Therefore, Majed must rub the stones **6 times** to have at least 100 stones. **Final answer:** Majed must rub the stones **6 times** to have 100 or more stones.