Question 1

Folding paper repeatedly doubles its thickness, leading to very rapid growth, but physical limits prevent many folds.

Step 1 — The Power of Folding

When we fold a piece of paper, its thickness doubles with each fold. This is an example of exponential growth.

Let us assume a standard paper thickness is about $0.1 \text{ mm}$.

After 1 fold, the thickness becomes:

$0.1 \text{ mm} \times 2^1$

$= 0.2 \text{ mm}$

After 2 folds, the thickness becomes:

$0.1 \text{ mm} \times 2^2$

$= 0.4 \text{ mm}$

After 3 folds, the thickness becomes:

$0.1 \text{ mm} \times 2^3$

$= 0.8 \text{ mm}$

After 4 folds, the thickness becomes:

$0.1 \text{ mm} \times 2^4$

$\boxed{1.6 \text{ mm}}$

We can see the thickness grows very quickly.

Step 2 — Reaching the Moon (Theoretically)

Let us use the initial paper thickness $T_0 = 0.1 \text{ mm}$. We need to convert this to meters: $0.1 \text{ mm} = 0.1 \times 10^{-3} \text{ m} = 10^{-4} \text{ m}$.

The average distance to the Moon is about $384,400 \text{ km}$. We convert this to meters: $384,400 \text{ km} = 384,400 \times 1000 \text{ m} = 3.844 \times 10^8 \text{ m}$.

The thickness after $n$ folds is given by $T_n = T_0 \times 2^n$. We want to find if $T_{46}$ is greater than or equal to the Moon's distance.

Let us calculate the thickness after 46 folds:

$T_{46} = 10^{-4} \text{ m} \times 2^{46}$

We know that $2^{10}$ is approximately $10^3$. So, $2^{46} = 2^6 \times 2^{40} = 64 \times (2^{10})^4 \approx 64 \times (10^3)^4 = 64 \times 10^{12}$.

$T_{46} \approx 10^{-4} \text{ m} \times 64 \times 10^{12}$

$T_{46} \approx 64 \times 10^8 \text{ m}$

$T_{46} \approx 6.4 \times 10^9 \text{ m}$

$\boxed{6.4 \times 10^9 \text{ m}}$

Since $6.4 \times 10^9 \text{ m}$ is much larger than $3.844 \times 10^8 \text{ m}$, the owl's statement is theoretically correct.

Step 3 — Practical Limitations of Folding

While theoretically possible, folding paper many times is practically impossible due to several reasons:

The paper becomes too thick. Each fold doubles the thickness, making it harder to bend.

The paper's area shrinks. Each fold halves the paper's surface area, making it too small to fold further.

The force required increases. As the paper gets thicker and smaller, more force is needed to make a crease.

For a standard sheet of paper, like A4 size, the maximum number of folds is typically 7 or 8 times. This is a common observation.

If we use thinner paper, like newspaper or tissue paper, we can fold it a few more times. Thinner paper is more flexible and takes up less space per fold. For example, a very large sheet of thin paper has been folded up to 12 times in experiments. However, even with very thin and large paper, there is still a physical limit.

Answer

(i) Theoretically, a paper can be folded about 42 to 46 times to reach the Moon's distance, as its thickness grows exponentially. (ii) Practically, a standard sheet of paper can be folded a maximum of 7 to 8 times. (iii) Using thinner paper, like newspaper or tissue paper, allows for a few more folds, typically up to 9 to 12 times, before it becomes too thick and small to fold further.