NCERT Solutions Ganita Prakash (Part 2) Chapter 6 .2 Thinking about ‘Think of a Number’ Tricks — In-text Questions

Book page 1376 Updated on2026-09-05

Q1.

Mukta thinks of another date, follows the same steps, and reports her answer as 1390. What date did Mukta start with this time?

Answer

25 December.

100M + 165 + D = 1390
100M + D = 1390 – 165 = 1225
Last two digits → D = 25 ; what comes before → M = 12
25/12 — 25 December

Why it happens: 1225 = 100 × 12 + 25. Because D is at most 31 it can never reach the hundreds place, so splitting 1225 after the last two digits is the only possible split — the month and the day cannot be confused.

Check it yourself: run 25/12 forward. 12 × 5 = 60, + 6 = 66, × 4 = 264, + 9 = 273, × 5 = 1365, + 25 = 1390. ✓

Q2.

Find the dates if the final answers are the following: (i) 1269 (ii) 394 (iii) 296

Answer

Subtract 165 from each answer, then read the last two digits as the day and the rest as the month.

Final answer	Answer – 165	Month M	Day D	Date
(i) 1269	1104	11	04	4 November
(ii) 394	229	2	29	29 February
(iii) 296	131	1	31	31 January

(i) 1269 – 165 = 1104 = 100 × 11 + 04 → 4/11
(ii) 394 – 165 = 229 = 100 × 2 + 29 → 29/02
(iii) 296 – 165 = 131 = 100 × 1 + 31 → 31/01

Did you know? 29 February only exists in a leap year, so the friend who gave the answer 394 was born on a leap day — a birthday that comes round only once in four years.

Why it happens: each answer is 100M + 165 + D. Removing the 165 leaves 100M + D, and since 0 < D ≤ 31 the day always fits inside the last two digits. Splitting the remainder there recovers M and D uniquely.

Q3.

Can you change the steps in this trick and still find the original date? Instead of subtracting 165 from the final answer, you might have to subtract some other number.

Answer

Yes. Only one thing really matters: the numbers you multiply the month by must have product 100. Everything you add along the way just piles up into one constant, and that is the number to subtract at the end.

Here is a shorter trick. Multiply the month by 5, add 3, multiply by 20, then add the day:

5M
5M + 3
(5M + 3) × 20 = 100M + 60
Add the day: 100M + 60 + D
So subtract 60, not 165.

Test it on 26 January: 1 × 5 = 5, + 3 = 8, × 20 = 160, + 26 = 186. Then 186 – 60 = 126 → M = 1, D = 26. ✓

Why it happens: suppose the multipliers are m₁, m₂, m₃ and the numbers added are k₁, k₂. The month ends up as m₁m₂m₃ × M, so the product must be 100 for the month to land in the hundreds place. The constant is k₁m₂m₃ + k₂m₃ — in the original trick 6 × 4 × 5 + 9 × 5 = 120 + 45 = 165, and in the new one 3 × 20 = 60.

Try This: multiply by 2, add 3, multiply by 10, add 7, multiply by 5, add the day. The month becomes 2 × 10 × 5 = 100 times itself, and the constant is 3 × 10 × 5 + 7 × 5 = 150 + 35 = 185. So subtract 185.

Q4.

Try to devise your own ‘Think of a Number’ trick.

Answer

Design it backwards: decide what expression you want at each stage, then write the instruction that produces it.

A trick that always ends at 7:

Say this out loud	What it does to x
Think of a number	x
Add 5	x + 5
Multiply by 4	4x + 20
Subtract 8	4x + 12
Divide by 4	x + 3
Add 4	x + 7
Subtract the number you thought of	7

A trick that hands the number back:

Think of a number: x
Multiply by 6: 6x
Add 18: 6x + 18
Divide by 3: 2x + 6
Subtract 6: 2x
Halve it: x — “You started with that number!”

Why it happens: a ‘predict the answer’ trick needs the x-terms to vanish, so the step before the last must leave exactly one x plus a constant, and the last step subtracts that one x. A ‘guess your number’ trick needs the opposite — the constants must vanish and exactly one x must be left. Writing the expression beside every instruction is what lets you control this; without it you are only guessing.

Tip: keep divisions honest. If you say “divide by 4”, make sure the expression really has a multiple of 4 in every term — as 4x + 12 does — otherwise your friend will be stuck with fractions.

Was this helpful? Report an error