Where should we place the mirror in shape A to get the shapes given below? A 1 2 3 4 5 6 Shape A, and the six shapes numbered 1 to 6.

Shape A is made of 2 squares side by side. Stand the mirror upright on shape A and look at the part in front of the mirror together with its reflection. A 1 2 3 4 5 6 Shape A and the six shapes to be made from it. Shape Where to keep the mirror on A What you see 1 Upright, across the middle of one square half square + half square = 1 square 2 Upright, on the line between the two squares 1 square + 1 square = 2 squares 3 Upright, along the slanting diagonal of the second square the L-shape of 3 squares 4 Upright, across the middle of the second square 1½ + 1½ = 3 squares in a row 5 Lying along the long side (top or bottom edge) of A 2 + 2 = a 2 by 2 square 6 Upright, at the short end edge of A 2 + 2 = 4 squares in a row Why it happens: A mirror hides everything behind it and shows a copy of everything in front of it. So you always see the front part twice — once real and once in the mirror. Try This: Shape 3 is the tricky one. Keep the mirror along the slanting corner-to-corner line of one square and peep — the L-shape appears.

NCERT Solutions for Class 4th Maths Chapter 11 . Games with a Mirror — Games with a Mirror

Book page 1682 Updated on2026-09-19

Q1.

Where should we place the mirror in shape A to get the shapes given below?

Shape A, and the six shapes numbered 1 to 6.

Answer

Shape A is made of 2 squares side by side. Stand the mirror upright on shape A and look at the part in front of the mirror together with its reflection.

Shape A and the six shapes to be made from it.

Shape	Where to keep the mirror on A	What you see
1	Upright, across the middle of one square	half square + half square = 1 square
2	Upright, on the line between the two squares	1 square + 1 square = 2 squares
3	Upright, along the slanting diagonal of the second square	the L-shape of 3 squares
4	Upright, across the middle of the second square	1½ + 1½ = 3 squares in a row
5	Lying along the long side (top or bottom edge) of A	2 + 2 = a 2 by 2 square
6	Upright, at the short end edge of A	2 + 2 = 4 squares in a row

Why it happens: A mirror hides everything behind it and shows a copy of everything in front of it. So you always see the front part twice — once real and once in the mirror.

Try This: Shape 3 is the tricky one. Keep the mirror along the slanting corner-to-corner line of one square and peep — the L-shape appears.

Q2.

Circle the numbers whose mirror image is the same number.

Answer

Circle the two boxes with 181. The two boxes with 686 should not be circled.

The four boxes printed in the book. The straight line in each box shows where the mirror is kept.

Box	Number	Mirror kept	Image	Circle it?
1	181	below the number	181	Yes
2	181	at the side	181	Yes
3	686	at the side	not a number	No
4	686	below the number	not a number	No

Why it happens: In 181 every digit — 1, 8, 1 — looks the same in a mirror, and the number reads the same from either end. In 686 the digit 6 turns into a backward 6, which is not a digit at all.

Q3.

Which digits from 0 to 9 have the same mirror image? ___________________

Answer

0, 1 and 8 when the mirror is kept at the side.

0, 1, 3 and 8 when the mirror is kept above or below the digit.

Digit	Mirror at the side	Mirror above or below
0	same	same
1	same	same
3	changes	same
8	same	same
2, 4, 5, 6, 7, 9	change	change

Why it happens: A digit stays the same in a mirror only when it can be folded on that line and both halves match. 0, 1 and 8 can be folded down the middle. 3 can be folded across the middle.

Check it yourself: Write 0 1 3 8 in big block letters and stand a mirror at their side, then below them.

Q4.

Make some 4-digit numbers such that the mirror image is the same number. Where would you keep the mirror in each case? How many such numbers can you make?

Answer

Keep the mirror at the side of the number. Then use only the digits 0, 1 and 8, and make the number read the same from both ends.

The 4-digit number looks like a b b a
The first digit a can be 1 or 8 (not 0) → 2 ways
The middle digit b can be 0, 1 or 8 → 3 ways
2 × 3 = 6 numbers

All six numbers are:

1001

1111

1881

8008

8118

8888

So you can make 6 such 4-digit numbers with the mirror kept at the side.

Why it happens: A side mirror turns the number back to front. So the last digit must look like the first, and the digits themselves must not change in a mirror.

Try This: If you keep the mirror below the number instead, the order of the digits does not change. Then you may use 0, 1, 3 and 8 in any order, and many more numbers are possible — 3108, 1380, 8310 and so on.

Q5.

Guess my number. It is a 3-digit number near 120 whose mirror image is the same number. Where is the mirror kept?

Answer

The number is 111, and the mirror is kept at its side.

Digits that do not change in a side mirror: 0, 1, 8
3-digit numbers near 120 made only of these: 101, 111, 181
111 is the nearest to 120.

111 reads the same from both ends, and each 1 looks like a 1 in the mirror. So its mirror image is 111 again.

Why it happens: A side mirror reverses the order of the digits. The number must read the same forwards and backwards, and every digit must be a mirror-safe one.

Did you know? 118 also works, but only if the mirror is kept below the number — then 1, 1 and 8 each stay the same and the order does not change.

Q6.

Make similar questions and ask your friends to guess the numbers.

Answer

Make your own puzzle in three steps.

Pick a number that does not change in a mirror, such as 808, 1881 or 8118.
Think of a nearby round number to give as a clue, such as “near 800” or “near 1900”.
Ask the question without telling where the mirror is kept.

Sample answer: “Guess my number. It is a 3-digit number near 800 whose mirror image is the same number. Where is the mirror kept?” — The answer is 808, with the mirror at the side.

Tip: Keep a small mirror ready so your friend can check the answer straight away.

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