Question

Shown are letters A–Z in a stylised alphabet. How many of these, if flipped along the horizontal axis, can still be read as capital letters?

Hint:

For mirror–flip puzzles, count (i) letters with horizontal symmetry and (ii) pairs that map to another valid capital (like \(M\!\leftrightarrow\!W\)). Tally both.

Answer 1

A letter qualifies if its horizontal mirror is either the same capital letter or a different valid capital letter.

Step 1: Self–mirrors across a horizontal axis
These letters remain the same when flipped top-to-bottom (they are vertically symmetrical in this stylized set of letters). The set of these letters is as follows:
\[ \{B, C, D, E, H, I, K, O, S, X, Z\} \] This set includes 11 letters that, when reflected horizontally, do not change and remain the same capital letter. These letters are symmetrical along the horizontal axis. Therefore, the number of self-mirroring letters is 11.

Step 2: Pair–mirrors that turn into another capital
These are pairs of letters that, when flipped horizontally, transform into another capital letter. The following pair of letters meets this criterion:
\[ M \leftrightarrow W \] The letter M mirrors to form W, and W mirrors to form M. Therefore, this pair of letters gives us 2 letters that qualify as having a horizontal mirror image of a different capital letter.

Additionally, the letter N has a unique property in that its shape remains unchanged when flipped horizontally. While it may appear that the letter should have a partner mirror, the diagonal form of N remains valid after a flip, making it its own valid mirror image.
Thus, we have 1 letter (the letter N) that remains unchanged when flipped horizontally, further contributing to our total.

Step 3: Total
Now, we add up the total number of letters that qualify:
- 11 letters from Step 1 (self-mirroring letters),
- 2 letters from Step 2 (pair-mirroring letters),
- 1 letter from Step 2 (the letter N that is its own mirror).
Thus, the total number of letters that qualify is:
\[ 11 + 2 + 1 = \boxed{14}. \]