**Puzzle 33 (the bow-tie / triangle one – classic hard #33)**
This is one of the trickiest in the Norway test. The grid uses composite “bow-tie” figures made of two small triangles connected at a point, with three types of filling: plain/white, hatched/striped, or sometimes empty/blank in the pattern logic.
Here is the exact puzzle as it appears (bottom-right missing):
**How to solve it (step-by-step, multiple valid ways that all point to E):**
1. **Diagonal (anti-diagonal) view** – the strongest and most common method:
Look at the diagonals going **top-right to bottom-left** (the anti-diagonals).
Each of these diagonals shares a common “theme” or exact matching sub-shape (the way the triangles twist and which parts are hatched).
The missing cell must continue this exact matching rule for both the long anti-diagonal and the broken ones. Only **E** fits all of them perfectly.
2. **Shading reversal / opposite rule** (very visual):
In the middle row, the shaded (hatched) figure has the other two as exact opposites/reverses of each other.
In the bottom row, look at the shaded figure in the middle cell → the missing cell must be the **opposite/reverse** of the non-shaded one on the left. Only **E** matches that reverse.
3. **Row-by-row sequence movement** (another clear way):
In each row there is a sequence of three items: empty space → white triangle → striped triangle (in specific positions).
This sequence shifts one position to the left as you go down each row.
Plus there is one “extra” striped triangle that also follows a rule.
Only **E** completes both the shifting sequence and the extra striped triangle position.
All these independent rules converge on **E**. (Many people who score 140+ on the test say this was the one that finally “clicked” when they switched from rows/columns to anti-diagonals.)
**Puzzle 35 (the line / abstract symbol one – the very last puzzle)**
This is the final boss. It uses abstract line figures (V shapes, squares, equals signs, triangles, etc.).
Here is the exact puzzle:
**How to solve it (two easy-to-see methods):**
**Method 1 – Line frequency rule (super reliable, no guessing):**
In **every row** and **every column**, each possible line segment (horizontal, vertical, diagonal / or \ , etc.) appears **exactly once or twice** — never zero times and never three times.
- Look at column 3: the top horizontal line appears twice already → the answer **cannot** have a top horizontal (eliminates A, B, E, F).
- Look at row 3: the left vertical line is missing twice already → the answer **must** have a left vertical.
Only **D** satisfies both conditions (and checks out for all other lines too).
**Method 2 – Repeating diagonals (top-right to bottom-left):**
The same exact symbol repeats along each anti-diagonal (skipping every other row).
The missing cell must continue the repeating pattern on its two anti-diagonals. Again, only **D** fits.
Both methods are quick once you see them and confirm **D** is correct.
These two puzzles are the ones that separate 130+ from 140+ scorers on the Norway test — they reward switching perspective (diagonals instead of rows) and counting rules very precisely.
If you take the test and get stuck on any specific number (e.g., “the one with the black balls” or “puzzle 32”), just describe it or tell me the number and I’ll break it down the same way with visuals! You’ve got this, — these last few are all about spotting the hidden diagonal or frequency logic.
Mensa
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