EN हिं

NCERT Solutions for Class 7th Maths Chapter 7 Puzzle page — A Magic Trick

Book page 190 Updated on2026-09-19

Q1.
Think of any number. Now multiply it by 2. Add 10. Divide by 2. Now subtract the original number you thought of. Finally, add 3. I predict that you now have 8. Am I correct? Can you explain why the trick works? [Hint: Denote the first number thought of by x.]
Answer

Yes, the prediction is always correct — the answer is 8 whatever number you start with.

Let the number you think of be x, and follow the steps in algebra.

StepExpressionIf x = 7If x = 100
Think of a numberx7100
Multiply it by 22x14200
Add 102x + 1024210
Divide by 2x + 512105
Subtract the original numberx + 5 − x = 555
Add 35 + 3 = 888
Why it happens: look at the fourth line. Dividing 2x + 10 by 2 gives x + 5 — both terms are halved, which is why the 10 becomes 5. Now the expression carries exactly one x, and the next step takes that x away. From that moment the number you chose has vanished completely, so the finish, 5 + 3 = 8, cannot depend on it. This is what algebra is for: one line of symbols proves a fact about every starting number at once, which no amount of testing could do.
Check it yourself: try a negative number. x = − 6 → − 12 → − 2 → − 1 → − 1 − (− 6) = 5 → 8. ✓ It even works with fractions.
Q2.
Try the trick on your friends and family! Can you make your own such tricks?
Answer

Yes. The recipe is simple: build up an expression, then make sure the x cancels out at the end.

How to design one

  1. Start with x.
  2. Do some steps that keep exactly one x, such as "multiply by 4, add 20, divide by 4" — this gives x + 5.
  3. Ask for the original number to be subtracted. Now only a plain number is left.
  4. Add or subtract anything you like to land on the number you want to predict.
Your own trick — try this one
Think of a number  → x
Multiply by 3  → 3x
Add 12  → 3x + 12
Divide by 3  → x + 4
Subtract the number you thought of  → 4
Add 6  → 10
Prediction: the answer is always 10.
A doubling trick
Think of a number → x  | Double it → 2x  | Add 8 → 2x + 8  | Halve it → x + 4  | Take away the original number → 4
Prediction: the answer is always 4.
Why it happens: the trick works because of the step that halves (or divides) the whole expression. Dividing 2x + 8 by 2 halves both parts, giving x + 4 — one x, and a leftover number. Subtracting the original number then removes the x, and the leftover number is the answer you predicted from the start.
Tip: when you test your trick, use three very different starting numbers — a small one, a large one and a negative one. If all three give the same answer, your algebra is right.
Was this helpful?