How Many Triangles Puzzle: Answers and the Counting Trick
The answer to the classic how many triangles puzzle (one big triangle with two lines fanning down from the top and one line across the middle) is 12. Most people say 8 or 10 because they miss the triangles made of several smaller pieces. Below is the full answer, plus a counting trick that works on almost any "how many triangles do you see" picture.
If you always end up with a different number than your friends and can't tell why, IQ Tester shows how your pattern and logic skills compare to your other strengths: Find my weak spots.
The classic how many triangles puzzle
Since there are a hundred versions of this picture online, here's the one we're solving, described so you can draw it:
- Draw a big triangle, point at the top.
- From the top point, draw two lines down to the base, so the top is split into three thin slices.
- Draw one straight horizontal line across the triangle, about halfway down, crossing all the slices.
Now: how many triangles are there?
Take a minute. Write your number down before reading on.
The answer, explained
12 triangles.
Here's why. Every triangle in this picture has its point at the top and its bottom edge sitting on either the middle line or the base.
Triangles that end at the middle line:
- 3 single slices
- 2 made of two slices side by side
- 1 made of all three slices
That's 6.
Triangles that end at the base: exactly the same pattern, just taller. Another 6.
6 + 6 = 12.
The shapes between the middle line and the base aren't triangles. They have four sides (trapezoids), so they don't count. That's where a lot of people over-count.
A counting method that always works
Here's the triangle counting trick, the part most "how many triangles puzzle solution" pages skip. It works for any picture where lines fan out from one point.
Step 1: count the lines from the top point
Include the two outer sides. In the classic puzzle, that's 2 sides + 2 inside lines = 4 lines.
Step 2: count the pairs
Any two of those lines make one triangle (per level). The number of pairs from 4 lines is 4 x 3 / 2 = 6.
| Lines from the top | Pairs (triangles per level) |
|---|---|
| 2 | 1 |
| 3 | 3 |
| 4 | 6 |
| 5 | 10 |
| 6 | 15 |
The rule: lines x (lines − 1) / 2.
Step 3: multiply by the number of levels
Count the horizontal lines, including the base. Classic puzzle: middle line + base = 2 levels.
6 x 2 = 12. Same answer, zero chance of missing one.
For pictures that don't fan from one point
Use the size sweep instead:
- Count every triangle made of one piece.
- Then every triangle made of two pieces.
- Then three, four, and so on, up to the whole shape.
- Label pieces with letters (A, B, C...) and write each triangle as a list ("ABC"). No list, no count.
It's slow. It's also the only way that's reliable on a messy picture.
More triangle puzzles with answers
Here's a mini answer key for more triangle puzzles for adults and teens. Draw each one first.
Puzzle 2: the bigger fan
A triangle with three lines from the top (5 lines total including sides) and two horizontal lines across it (3 levels including the base).
Answer: 30. 5 lines give 10 pairs, times 3 levels.
Puzzle 3: the four-piece triangle
Join the midpoints of a triangle's three sides, so it splits into four smaller triangles (three pointing up, one upside down in the middle).
Answer: 5. Four small ones plus the big one.
Puzzle 4: the triangle grid
Split each side of a triangle into three equal parts and draw lines parallel to the sides, making a grid of 9 tiny triangles.
Answer: 13.
- Pointing up: 6 tiny, 3 medium (made of 4 tiny), 1 big = 10
- Pointing down: 3 tiny = 3
The upside-down ones are what everyone forgets. If you split each side into four parts instead, the answer jumps to 27.
Puzzle 5: the square with diagonals
Draw a square, then both diagonals.
Answer: 8. Four small triangles meet in the middle. Each diagonal also cuts the square into two big triangles, and there are two diagonals, so that's 4 more.
Puzzle 6: the six-pointed star
How many triangles in a Star of David (two overlapping triangles)?
Answer: 8. Six small points plus the two big triangles.
| Puzzle | Answer | What people usually miss |
|---|---|---|
| Classic fan | 12 | Triangles made of two or three slices |
| Bigger fan | 30 | The taller triangles ending at lower levels |
| Four-piece | 5 | The big outer triangle |
| Triangle grid (3 per side) | 13 | The three upside-down ones |
| Square + diagonals | 8 | The four half-square triangles |
| Six-pointed star | 8 | The two big overlapping triangles |
Why everyone gets a different number
The "how many triangles do you see" posts go viral for a reason: the comments are chaos. Here's why people disagree:
- They only count single pieces. Your eyes see regions, not combinations.
- They count trapezoids. Four sides means not a triangle, no matter how pointy it looks.
- They miss upside-down triangles. Your brain expects points on top.
- They lose their place. Counting in your head without labels means doubles and skips.
- The picture is ambiguous. Some viral images have lines that almost meet. If two lines don't actually touch, the triangle doesn't exist.
That last one is why a "how many triangles riddle answer" can honestly differ between versions of the same image. Always check where the lines really end.
And honestly, the hardest part isn't the counting. It's knowing whether you're the person who rushes and misses pieces, or the person who's slow but accurate. You can't see that about yourself from one puzzle.
IQ Tester's pattern and logic questions show you. It gives 20 untimed questions across number series, verbal analogy, logic and pattern, easiest first, with skips counted as wrong, then shows your strength in each category. The guides follow up with a short daily drill on whichever is weakest. Find my weak spots
Similar visual puzzles to try
If counting triangles is your thing, try these next:
- Count the squares in a 4x4 grid (answer: 30, from 16 + 9 + 4 + 1). Same size-sweep trick.
- Hard emoji odd one out grids, which train scanning instead of counting. We've got 30 in our find the odd one out emoji (hard) set.
- The nine-dot puzzle and other puzzles that look easy but are actually hard.
Check your pattern brain in the next few minutes
You've got the how many triangles puzzle answer and a trick that always works. Now see how your pattern skills stack up against your number, verbal and logic reasoning. IQ Tester gives you your band plus three of your four category strengths for free, untimed, so slow-and-careful counters aren't punished. Then challenge the friend who said "8" head-to-head.
FAQ
How many triangles are there in the classic triangle puzzle?
In the version with two lines fanning from the top and one line across the middle, there are 12 triangles. Six end at the middle line and six end at the base. Other versions have different answers, so check how many lines your picture has.
What is the trick to counting triangles?
For pictures where lines fan from one point, count the lines from that point (including the sides), work out lines x (lines − 1) / 2, then multiply by the number of horizontal levels. For any other picture, count by size: one piece, two pieces, three pieces, and label each piece with a letter.
How many triangles are in a square with both diagonals?
Eight. There are four small triangles meeting in the center, plus four big ones, because each diagonal splits the square into two halves.
Why do people get different answers to "how many triangles do you see"?
Most people count only single pieces, miss upside-down triangles, or count four-sided shapes by mistake. Some viral pictures are also drawn so lines almost touch, which makes the answer depend on how you read the image.
Are triangle counting puzzles on IQ tests?
Counting-figure questions show up in some aptitude and reasoning tests, and they use the same skills as pattern questions: careful scanning and spotting structure. IQ Tester's pattern category tests that kind of thinking, but it's for fun, not a clinical assessment.