Letters and digits

In your book, Maths Mela (Chapter 10), we sort letters and digits by the symmetry they have. A shape can have reflection symmetry (a line of symmetry, so its two halves match when folded), rotational symmetry (it looks the same after less than a full turn), both, or neither.

The capital letter H has both: a vertical and a horizontal line of symmetry, and it looks the same after 1/2 a turn. The capital letter I, drawn in the book as one plain straight bar, has both too: it can be folded down its middle or across its middle, and after 1/2 a turn it looks the same. The capital letter X also has both: it has a vertical and a horizontal line of symmetry, and it looks the same after 1/2 a turn. The capital letter Y has only reflection symmetry: a vertical line down its middle, but after 1/2 a turn it is upside down, with its two arms at the bottom. The capital letter N has only rotational symmetry: no line of symmetry, but after 1/2 a turn it looks like an N again.

Now the digits, drawn the way the book draws them: 1 as a plain straight bar, 0 as an oval, and 8 as two equal round loops, one on top of the other. These three digits have both kinds of symmetry: each has a vertical and a horizontal line of symmetry, and each looks the same after 1/2 a turn. The digit 7 has neither: no fold makes its halves match, and after 1/2 a turn it is upside down.

Numbers made of such digits can have symmetry too. The number 11 has a vertical line between the two 1s and a horizontal line across the middle, and it looks the same after 1/2 a turn: it has both. The same is true of 1001. But the number 10 has only reflection symmetry: a horizontal line across its middle works, but after 1/2 a turn it reads 01.