Mirror and water images for AFCAT: letters, numbers, words and clocks

Mirror and water image questions show you a word, a number, a figure or a clock face and ask what its reflection looks like. They are among the fastest questions in the non-verbal part of AFCAT, often under 20 seconds each, provided you know exactly what each kind of reflection does. The errors come from mixing the two up, or from reversing the letter order but forgetting to flip each letter.

This guide covers both reflections, the letters and digits that do not change, words and numbers, and clocks, where a simple subtraction does the work.

Two kinds of reflection

A useful check: in a mirror image, the top of the figure is still at the top. In a water image, the left end is still at the left.

Letters that do not change

These lists assume plain capital letters with no serifs.

Note N, S and Z. They look the same after a half-turn but change under either reflection on its own.

Lowercase letters rarely look the same after a reflection, and some change into other letters. A mirror turns b into d and p into q. Water turns b into p and d into q.

For digits in a plain font, 0 and 8 look the same in a mirror. 0, 3 and 8 look the same in water. The digit 1 depends on the font, so do not rely on it.

Words and numbers

Mirror image of a word: the letter order reverses and every letter is flipped left–right. Symmetric letters look unchanged, but they still move to their new position.

Example 1. Describe the mirror image of AIR.

• The order reverses to R, I, A.
• A and I are symmetric, so they look normal.
• R is flipped, with its bowl and leg facing left.

Example 2. Which word looks exactly the same in a mirror: TOT, NUN, DAD, BOB?

• The word must be a palindrome made only of mirror-symmetric letters.
• NUN fails on N, DAD on D and BOB on B. TOT passes: T and O are symmetric, and it reads the same both ways.

Water image of a word: the letter order stays the same and every letter is turned upside down.

Example 3. Which word looks exactly the same in water: BIKE, BAKE, BITE, BONE?

• Every letter must be in the water list: B, C, D, E, H, I, K, O, X.
• BAKE fails on A, BITE on T and BONE on N. BIKE passes.

Example 4. Describe the mirror image of the number 2025.

• The order reverses to 5, 2, 0, 2.
• 0 looks normal. Every 2 and the 5 appear back to front.

Clocks in a mirror

For the mirror image of an analogue clock, subtract the time from 11:60 (which is simply 12:00, written so the minutes subtract easily).

Why it works: a vertical mirror sends a hand at angle θ from 12 to angle 360° − θ, which is the same as counting the time backwards from 12. So the image time is 12:00 minus the real time. This is exact, not an approximation, because both hands reflect consistently.

Example 5. A clock shows 3:40. What does its mirror image show?

• 11:60 − 3:40 = 8:20.

Example 6. A clock shows 2:15. Its mirror image?

• 11:60 − 2:15 = 9:45.

Example 7. A clock shows 12:20. Its mirror image?

• The time is past 12, so subtract from 23:60 instead: 23:60 − 12:20 = 11:40.

The same rule works backwards. If the mirror shows 8:20, the real time is 11:60 − 8:20 = 3:40.

Only 6:00 and 12:00 look the same in a mirror, because those are the only times when both hands lie on the vertical 12–6 line.

Clocks in water

For the water image of a clock, most books use the rule: subtract the time from 18:30, and take away 12 from the hours if the result is 12 or more.

Example 8. A clock shows 3:00. Its water image?

• 18:30 − 3:00 = 15:30, which is 3:30 on a 12-hour dial.

Check it by picturing the dial: the minute hand at 12 reflects to 6, and the hour hand at 3 stays at 3. The dial reads roughly half past three.

Practice set

1. A clock shows 10:25. What does its mirror image show?
2. A clock shows 6:00. What does its mirror image show?
3. A mirror shows a clock at 4:50. What is the real time?
4. Which letter looks the same in both a mirror and water: A, H, M, U?
5. Which word looks the same in water: DECK, DUCK, DARK, DESK?
6. Which of these capitals change under both a mirror and water, but look the same after a half-turn: A, N, O, T?
7. Describe the mirror image of the word OTTO.
8. A clock shows 7:10. Using the 18:30 rule, what is its water image?

Answers:

1. 11:60 − 10:25 = 1:35.
2. 11:60 − 6:00 = 5:60 = 6:00.
3. 11:60 − 4:50 = 7:10. The rule works both ways.
4. H. A, M and U are mirror-symmetric but not water-symmetric.
5. DECK. D, E, C and K are all in the water list. DUCK fails on U, DARK on A and R, DESK on S.
6. N. O looks the same in all three; A and T survive a mirror.
7. It looks exactly the same. O and T are mirror-symmetric, and OTTO is a palindrome.
8. 18:30 − 7:10 = 11:20.

What to do next

• Write the two letter lists (mirror and water) from memory until you get both right twice in a row.
• Do 20 clock mirror questions in one sitting, aiming for under 10 seconds each.
• Practise word and number images with options that differ only in one flipped letter. That is where marks are lost.
• Continue with paper folding and cutting, which uses the same reflection idea across fold lines, and figure analogy.