Hold this page up to a mirror and the words run backwards. That swap has one simple rule behind it. And once you can picture how shapes overlap, you can count hidden shapes too — a big triangle can be hiding five triangles at once!
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A mirror placed on the side swaps left and right. It does not flip anything upside down.
Three questions that look alike
| Question type | What changes |
|---|---|
| Mirror image | left ↔ right (mirror at the side) |
| Water image | top ↔ bottom (a reflection in a lake) |
| Rotation | the whole figure turns; nothing is reversed |
Top and bottom never change in a mirror. Hold your right hand up to a mirror — the reflection raises what looks like its left hand. But the top of your head is still at the top.
Try each one yourself first, on rough paper, before you check.
Some capital letters have a vertical line of symmetry, so they look exactly the same in a mirror.
Learn this list by heart
A H I M O T U V W X Y
Eleven capitals are unchanged in a mirror. Among digits, only 0, 1 and 8 are unchanged.
🪜 Mirroring a whole word
Fun fact: the whole word MATH is made only of symmetric letters (M, A, T, H) — so is TAXI! Try checking BIRD — only the I survives unchanged.
A clock in a mirror shows a different time — and a simple formula gives it instantly.
The mirror-time formula
Mirror time = 11:60 − the given time
Subtract the minutes first, then the hours — 11:60 − 3:00 gives 60 − 0 = 60 min and 11 − 3 = 8, so 8 hours and 60 minutes = 9:00.
Two special times: 12:00 mirrors to itself, and 6:00 also mirrors to itself — both sit exactly on the mirror line running through 12 and 6.
An embedded-figure question hides small shapes inside a bigger one. Count the smallest pieces first, then the pieces made by joining two together, then the whole figure.
Triangle split by midpoints
Join the midpoints of a triangle's 3 sides. You get 4 small triangles, and the original big one still counts — 5 triangles in total.
Square split by a cross
One line down the middle and one line across. You get 4 small squares plus the big one — 5 squares in total.
Rectangle split into 3
Two lines make 3 equal strips. Count 3 single strips, 2 double strips (joining neighbours), and 1 whole — 6 rectangles in total.
🪜 The counting method
12 IMO-style questions. There is no negative marking in the real paper, so never leave one blank. 🍀
