Question 1

We can use a variable to represent the unknown number. This helps us see how the trick works.

Step 1 — Following the Trick

Let us call the number you think of x. We will write down each step. Then we will see what the expression becomes.

Think of any number. $x$

Now multiply it by 2. $= x \times 2$ $= 2x$

Add 10. $= 2x + 10$

Divide by 2. $= \frac{2x + 10}{2}$ $= \frac{2x}{2} + \frac{10}{2}$ $= x + 5$

Now subtract the original number you thought of. $= (x + 5) - x$ $= 5$

Finally, add 3. $= 5 + 3$

$\boxed{8}$

Step 2 — Checking the Prediction

The final result of the trick is 8. The puzzle predicts that you now have 8. So, the prediction is correct.

Step 3 — Explaining Why the Trick Works

Let us look at the steps again. The original number was x. After dividing by 2, we had $x + 5$. Then we subtracted the original number x. The 'x' terms cancel each other out. So, the value of x does not matter. Only the numbers we added and divided remain. The trick always gives the same answer.

Step 4 — Making Your Own Trick

We can make a new trick. We need the original number to cancel out. Let us try to make a trick that always gives 10.

Think of any number. $x$

Multiply it by 3. $= 3x$

Add 15. $= 3x + 15$

Divide by 3. $= \frac{3x + 15}{3}$ $= x + 5$

Subtract the original number. $= (x + 5) - x$ $= 5$

Add 5. $= 5 + 5$

$\boxed{10}$

Answer

(i) Yes, the prediction is correct. (ii) The trick works because the original number (represented by x) cancels out during the steps. The final result depends only on the constant numbers used in the operations. (iii) Yes, we can make our own tricks. Here is one example:

Think of any number. Multiply it by 3. Add 15. Divide by 3. Subtract the original number. Add 5.

The final answer will always be 10.