IQ Test – Mensa-Style Visual Logic Puzzle #9

 Disclaimer: This content is inspired by Mensa-style IQ tests and is an unofficial practice puzzle.

It is not affiliated with or endorsed by Mensa International Ltd.
All visual designs and explanations are original creations by the author.

20.Difficulty level: 2 out of 5

This puzzle represents a easy-level question (around the #0-20 range)
commonly found in online Mensa-style IQ tests.
Pay close attention to the visual pattern variations.

18.Difficulty level: 3.5 out of 5

This puzzle represents a Middle-level question (around the #30 range)
commonly found in online Mensa-style IQ tests.
Pay close attention to the visual pattern variations.

19.Difficulty level: 3 out of 5

This puzzle represents a Middle-level question (around the #20 range)
commonly found in online Mensa-style IQ tests.
Pay close attention to the visual pattern variations.

Explanation #17 (click to expand)

Each matrix square is composed of 9 cells (a 3×3 grid), and its color is determined by the following diagonal calculation:

$$(1st\ cell \times 9th\ cell) - (3rd\ cell \times 7th\ cell)$$

(1st cell×9th cell)−(3rd cell×7th cell)

If the result is negative, the square is colored yellow,

and if the result is positive, it is colored blue.

B

Explanation #18 (click to expand)

In each row, Columns 1 and 2 are combined to determine the transformation value of the line (──) in Column 3.

• Result +1 → vertical line (ㅣ), rotated 90° counterclockwise

• Result +2 → horizontal line (ㅡ), rotated 180° counterclockwise

• Result +4 → 360° counterclockwise rotation (returns to the original form)

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Upper and Lower Block Rules

White and black squares are placed above and below the line.

Their interaction follows a simple cancellation rule:

✔ Fundamental Cancellation Rule

• One black square and one white square cancel each other out.

• Only the surplus squares (the color with more pieces) remain after cancellation.

• Identical colors do not interact and remain unchanged.

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✔ Upper Side

• Apply the cancellation rule between black and white squares.

• After cancellation, only the remaining white squares (if any) stay on the upper side.

✔ Lower Side

• The same cancellation rule is applied.

• After cancellation, any remaining black squares stay on the lower side.

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Rotation Based on Remaining Black Squares

If only black squares remain in Column 3 after all cancellations:

• The number of remaining black squares determines how far the right half of the line (──) rotates counterclockwise:

• 1 black square → 90° counterclockwise

• 2 black squares → 180° counterclockwise

• 3 black squares → 270° counterclockwise, and so on.

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Final Adjustment Rule

When evaluating Column 3:

• Any black square that remains on the lower side is flipped upward.

• During this flip, the square changes into a white square,
  except for the single black square used to determine the rotation value.

In other words:

Black squares below the line move upward as white squares, leaving only one black square in place for rotation calculation.

A

Explanation #19 (click to expand)

• The yellow shape moves clockwise,

  • by 2 cells in Column 2,

  • and by 3 cells in Column 3.

• The blue shape moves to the right,

  • by 3 cells in Column 2,

  • and by 5 cells in Column 3.

• The black shape moves to the left,

  • by 2 cells in both Column 2 and Column 3.

When multiple colors overlap in the same position,

the visibility priority is:

Yellow > Blue > Black

For example, in Row 1, Column 2,

there is a blue shape behind the yellow one,

but only the yellow shape is visible because it has the highest priority.

Mensa-Style IQ Test Guide

In the mid-section of Mensa-style IQ tests, problems often involve shape-interaction rules where one figure transforms when it meets another. The 30th question in the online Norway Mensa-style test is a good example of this. To solve such problems efficiently, pay close attention to how each shape changes upon contact with another.

Mensa-style IQ tests tend to feature relatively intuitive questions up to the late 20s, but starting from the 30s, problems that require calculation and logical reasoning begin to appear. As the test moves into the 40s, the questions often involve more complex and mixed rules, and this stage becomes the key point for time management during the actual exam.

To solve these mid-to-late questions efficiently, it’s important to familiarize yourself with a wide variety of pattern and logic puzzles in advance. In particular, focusing on problems in the mid-30s to 40s range of online Mensa-style tests is very effective for developing real test intuition.

According to testimonies from successful Mensa members, the exact passing criteria or number of correct answers has not been publicly disclosed, but it’s generally said that those who make only one to three mistakes tend to pass. Therefore, rather than simply solving quickly, it’s far more important to prioritize accuracy and careful reasoning.

We can find a wide variety of IQ test questions online, and some of them can be extremely complex and difficult. In fact, many of the problems I create here are also quite complicated or require a lot of calculation time. I’m not claiming that these kinds of questions actually appear on the real MENSA exam. This is simply my personal view, but MENSA questions tend to be much simpler and more straightforward.

Still, the reason for solving problems like these is… well, it’s part of developing your cognitive skills, and I believe it can serve as good practice for anyone who plans to challenge the MENSA test in the future.

🧠 How to Improve Your Mensa-Style Puzzle Solving Skills

Train Pattern Recognition
Practice identifying repeating rules across different shapes, colors, and directions.
Focus on noticing symmetry, rotation, reflection, overlap, and sequence progression — these five appear in over 80% of Mensa visual problems.

Think Like a Coder, Not an Artist
Try to “describe” each figure as a set of simple logical rules — for example, if A overlaps B, remove the edge, or rotate +90°.
The goal is to translate what you see into structured logic rather than rely on aesthetic intuition.

Use Dual Comparison Strategy
Don’t just compare horizontally (row-wise); always check columns as well.
Many puzzles hide their main rule diagonally, so practice scanning in multiple directions.

Slow Down at the Beginning
The first 10–15 seconds you spend decoding the pattern usually save more time later.
Rushing early often leads to misinterpretation of rules, especially when multiple transformations overlap.

Strengthen Visual Memory
Practice with short-term visual recall games — for example, memorize a 3×3 or 4×4 grid of colors for a few seconds,
then recreate it mentally. This helps you retain intermediate shapes and patterns without re-examining the puzzle every time.

Learn Common Rule Archetypes
Most Mensa-style puzzles are built on a few core transformation rules:

• Addition / Subtraction of shapes (parts appear or vanish when combined)

• Rotation + Reflection hybrids (mirror + turn effects)

• Alternating color dominance (color inversion or cyclic order)

• Positional shifts (movement along x/y or diagonal axes)

• Logical “XOR” patterns — shapes overlap only when one is filled and the other is empty.
  Knowing these archetypes helps you predict the rule type almost instantly.

Review Your Mistakes Intentionally
When you miss a question, don’t just look at the solution — reconstruct the logic yourself until the transformation feels intuitive.
This reflective step trains your mind to detect subtle rule combinations and prevents repeating the same error in future puzzles.

Maintain Calm Focus
Mensa tests measure not just reasoning but also emotional control under pressure.
A relaxed mind perceives spatial relationships faster and more accurately.
Practicing slow breathing or brief visualization before starting the test can noticeably improve clarity and consistency.