1. **Stating the problem:** Majed starts with 2 magic stones. Each time the stones are rubbed once, each stone produces one new stone, effectively doubling the total number of stones. 2. **Understanding the process:** After rubbing once, the number of stones doubles. So if $n$ is the number of times rubbed, the total stones after $n$ rubs is given by: $$\text{Total stones} = 2 \times 2^n = 2^{n+1}$$ because we start with 2 stones and each rubbing doubles the count. 3. **Setting up the equation:** We want to find $n$ such that the total stones equal 100: $$2^{n+1} = 100$$ 4. **Solving for $n$:** Take the logarithm base 2 of both sides: $$n+1 = \log_2(100)$$ 5. **Calculate $\log_2(100)$:** Since $100 = 10^2$, and $\log_2(10) \approx 3.3219$, then $$\log_2(100) = 2 \times 3.3219 = 6.6439$$ 6. **Find $n$:** $$n = 6.6439 - 1 = 5.6439$$ 7. **Interpretation:** Since $n$ must be an integer number of rubs, and the stones double only after each full rub, Majed must rub the stones 6 times to have at least 100 stones. 8. **Verification:** After 5 rubs: $2^{5+1} = 2^6 = 64$ stones (less than 100) After 6 rubs: $2^{6+1} = 2^7 = 128$ stones (more than 100) **Final answer:** Majed must rub the stones **6 times** to have at least 100 stones.