Mirror numbers

In your book, Maths Mela (Chapter 11), we stand a mirror beside a number and look at its reflection. A mirror beside a number turns it back to front. Which numbers still look the same?

Start with single digits. Write the digit one as a plain straight stroke. Then zero, one and eight look exactly the same in a mirror beside them, because their left half matches their right half. A six does not: in the mirror it faces the other way, back to front.

Now try 181. The mirror reverses the order, so the last digit comes first, and it flips each digit. The order 1, 8, 1 reads the same backwards, and one and eight do not change when flipped. So 181 looks the same in the mirror! But 686 does not, because each six turns back to front.

So a number looks the same in a mirror beside it only if it reads the same backwards and uses only zero, one and eight. The 4-digit numbers like that are 1001, 1111, 1881, 8008, 8118 and 8888. That is 6 numbers. (A 4-digit number cannot start with zero.)