How to Solve Mirror Image Puzzles: Clocks, Letters, Tiles and Light

To solve a mirror image puzzle, first decide which way the mirror flips the picture: a mirror standing beside it swaps left and right, while still water beneath it flips top to bottom. Then apply that single flip to every part of the picture in turn, whether it is a clock hand, a letter, a tile pattern or a beam of light, and check that nothing else has changed.

This guide covers the rules for clocks, digits, letters, tiles and light paths, a step-by-step method, full worked examples and three practice puzzles with answers.

What is a mirror image puzzle?

A mirror image puzzle shows a picture as it would look in a mirror or in still water and asks you to undo the flip. Sometimes you must name the real time on a reflected clock. Sometimes you must pick the one tile that is a mirror copy rather than a turned copy, or find the word that looks the same in a lake.

A related kind asks about light itself. A beam leaves a lamp, bounces once off a mirror and must reach a given point. Where on the mirror does it bounce?

The table compares the common types and the one flip that matters in each.

What changes in a mirror and what stays the same?

A mirror keeps sizes, distances and angles. It changes only the handedness of the picture. A shape that bends to the right will bend to the left in the glass, and a clock that runs clockwise will seem to run the other way.

A paper published on 14 March 2025 lists exactly eight moves that carry a square onto itself: four turns (no turn, a quarter turn, a half turn and three quarter turns) and four reflections ^[1]. The reflections use the horizontal line through the middle, the vertical line, and the two diagonals ^[1]. Together these eight moves form the symmetry group of the square, a group of order eight ^[1].

That list explains why tile puzzles work. Turning a tile on the table reaches only the four turns. The other four looks need a flip, and no amount of turning on the table will undo one, because every turn keeps the handedness of the pattern.

Puzzle pieces follow the same split. A free piece may be turned, moved and flipped over, while a one-sided piece may be turned and moved but never flipped ^[1].

Both tiles in this guide are like that. Each one has a mirror twin that you cannot reach by turning, and that twin is the answer you are looking for.

What is the step-by-step method?

1. Name the mirror. Is it upright beside the picture, or flat beneath it like water? The first swaps left and right, the second swaps top and bottom.

1. Find a fixed line. Everything on the mirror line stays put. On a clock in a side mirror, the 12 and the 6 stay where they are. In water, the 3 and the 9 stay.

1. Flip one feature at a time. Move each hand, letter or filled cell to the matching spot on the other side of the fixed line.

1. Check the order. A side mirror reverses the order of letters in a word as well as each letter.

1. Test turns before flips. In a tile puzzle, turn the original through its four positions first. A candidate that matches none of them is the mirrored one.

1. Read the result as a whole. Make sure the answer is a real time, a real word or a real tile, then check it once more against the picture.

How do you read a clock in a mirror?

A clock seen in a side mirror runs backwards, so the rule is subtraction. Take the time you see away from 12:00, which is easiest written as 11:60. The answer is the real time, after two small tidy-ups:

• If the minutes come to 60, write 00 and add one to the hour. A mirror showing 4:00 gives 7:60, which is 8:00.
• If the hour comes to 0 or less, add 12. A mirror showing 12:30 gives an hour of 11 minus 12, which is minus 1, and adding 12 makes the real time 11:30.

Worked example. A mirror shows a clock reading 4:35. Subtract it from 11:60.

• Hours: 11 minus 4 is 7.
• Minutes: 60 minus 35 is 25.

The real time is 7:25. A quick check: 4:35 plus 7:25 makes exactly 12:00, which is always true for a time and its side-mirror image.

The rule works because a side mirror swings each hand back from the 12 by exactly as far as it had moved forward. A time looks unchanged only when both hands lie on the vertical line through the 12 and the 6, and that happens at 12:00 and 6:00 and at no other whole minute.

Digital clocks behave differently, since the mirror flips each digit as well. Here is what a mirror does to digits built from the usual seven bars.

A mirrored 1 moves to the left side of its cell, but it still reads as a 1. The swap between 2 and 5 is easy to miss. A side mirror also reverses the order of the digits, so a reflected display must be read from right to left before you swap any 2s and 5s.

How does a clock look in water?

Water swaps top and bottom, so the 12 and the 6 trade places while the 3 and the 9 stay where they are. A hand that seems to point at mark k really points at mark 6 minus k, adding 12 if the result is zero or below. So 1 and 5 swap, 2 and 4 swap, and 7 and 11 swap.

Read the minute hand first, because it lands on clean marks. Then use it to settle the hour hand.

Worked example. In the water, the hour hand sits a little past the 4 and the minute hand points straight at the 9.

• The 9 lies on the fixed line, so the minute hand really points at 9: the real time is 45 minutes past an hour.
• The 4 really sits at the 2. A hand a little past the 4 in the water is really a little before the 2.
• An hour hand just before the 2 with the minute hand on 45 means the real time is 1:45.

One surprise is worth knowing. A water image never shows a perfectly correct clock. Take a real 3:00: in the water the hour hand stays on the 3, but the minute hand jumps from the 12 to the 6, which says half past. A real clock at half past three has its hour hand halfway to the 4, so the reflected hour hand is half a gap between marks out of place.

As the real clock runs on, both reflected hands move backwards at their usual speeds, so that half-gap error never closes. That is why the hour hand can look slightly odd, and why the minute hand is the safer guide.

Which letters and words survive a mirror?

In plain block capitals, some letters are symmetric about a vertical line and some about a horizontal line. Drawn in a simple blocky style, the sets are these, and you can check any of them by holding the letter up to a mirror.

The two mirrors set different tests for a whole word.

• Water keeps the order of the letters, so a word looks the same in a lake when every letter is in the water row. CODE and BOOKED both pass. BOOKS fails, because S changes.
• A side mirror reverses the order too. A word survives only if every letter is in the side-mirror row and it reads the same backwards. WOW passes. HAT has the right letters but comes out backwards, and KAYAK reads the same backwards but each K flips the wrong way.

Fonts vary, so treat the table as a guide for simple capitals and look closely at letters such as B, C, D and K when a puzzle draws them in its own style.

Here is a riddle that puts the water test to work: only one word looks the same in the lake, and you must say which.

How do you spot the mirrored tile?

Tile puzzles show one original pattern and several copies. All but one are turned copies; the odd one has been flipped. The safe method is to turn the original through its four positions and compare.

Worked example. Here is the original tile, with a filled square for each coloured cell and a dot for each blank cell.

Original: ■ ■ · · ■ ■ · ■ ·

Which of these four is a mirror image?

Step 1: pick a landmark. The original has a lone filled corner, top left, joined to the centre through the top middle cell. Everything else hangs off the centre.

Step 2: turn the original a quarter turn clockwise. The lone corner moves to the top right and the long bar becomes the middle row. That is tile A.

Step 3: turn it again. After a half turn the lone corner sits bottom right, which gives tile B. After three quarter turns it sits bottom left, which gives tile D.

Step 4: what is left? Tile C matches none of the four turns. Put it next to tile A: each row of C is the same row of A read from right to left. So C is A flipped left to right, a side-mirror copy, and C is the answer.

Why can no turn reach C? The original has only one filled corner, so a move that leaves it unchanged would have to keep that corner in place. The only such moves are doing nothing and the flip along the diagonal through that corner, and the diagonal flip sends the filled top middle cell to the blank middle left cell. So nothing but doing nothing leaves the pattern unchanged, and all eight of its looks are different.

How does light bounce off a mirror?

Light bouncing off a flat mirror follows one rule: the angle on the way in equals the angle on the way out. A paper published on 8 March 2024 states the same equal-angle rule for a ball that bounces once off the curved edge of a round table and reaches a second ball ^[2]. It says that question can be seen as a beam of light bouncing inside a round mirror ^[2].

For a straight mirror there is a neat trick. Reflect the point the beam must reach to the far side of the mirror line, then draw a straight line from the lamp to that copy. Where the straight line crosses the mirror is the bounce point.

Worked example. On a grid, the mirror lies along the bottom line. The lamp is at A, 4 squares up from the mirror at the left edge. The point B is 6 squares to the right of A and 2 squares up from the mirror.

• Reflect B in the mirror: its copy sits 6 squares right of A and 2 squares below the mirror.
• The straight line from A to the copy drops 6 squares while it moves 6 squares right, so it drops one square for every square across.
• It has dropped the 4 squares to the mirror after 4 squares across. The bounce point is 4 squares right of A, on the mirror.

Check the angles. From A to the bounce point the beam goes 4 across and 4 down, an angle of 45 degrees. From the bounce point to B it goes 2 across and 2 up, also 45 degrees. The path is as short as any one-bounce path can be: try any other bounce point on the mirror and the total length grows.

For one example position on a 12 by 6 rectangular table, the paper notes that a simple geometric method finds the one-bounce paths, and that particular position has four of them, one off each side ^[2]. On a round table it says the paths are not as simple to find, and it shows there are never more than four one-bounce paths for any position ^[2]. It also gives positions with exactly 0, 1, 2, 3 and 4 paths ^[2].

The mirror-copy trick above is our own way to handle a straight edge, and it is meant for straight edges only.

What mistakes should you avoid?

• Using the wrong flip. A water image is not a side-mirror image. Decide which line stays fixed before you start.
• Flipping letters but not their order. A side mirror reverses both.
• Trusting the hour hand. In a reflected clock, decode the minute hand first.
• Calling a turned tile a mirror tile. Always try all four turns of the original before deciding.
• Forgetting the 2 and 5 swap. On a digital display, these two digits change into each other in both kinds of mirror.

Can you solve these practice puzzles?

Practice 1: the clock. A clock seen in a side mirror reads 10:05. What is the real time?

Practice 2: the tile. Here is the original tile.

Original: ■ · ■ ■ · · ■ ■ ·

Four of these five can be turned on the table until they match the original exactly, and one of them needs no turn at all. Which one is the mirror image?

Practice 3: the word. Which of these words looks the same in a side mirror: AHA, KAYAK, MATH or BOOK?

Answers.

1. Subtract from 11:60: 11 minus 10 is 1, and 60 minus 5 is 55. The real time is 1:55. Check: 10:05 plus 1:55 is 12:00.
2. Tile D. Tile E is the original with no turn, A is a half turn, B is a quarter turn clockwise and C is a quarter turn the other way. Tile D is the original flipped top to bottom, a reflection that no turn can reach.
3. AHA. KAYAK contains K, MATH comes out backwards, and BOOK contains B and K, which change in a side mirror.

Each puzzle has exactly one answer, which you can confirm by testing every option in turn.

For one more reflection to decode, try this riddle: a clock is seen in the water, where top and bottom swap, and you must work out what time the real clock shows.