Visual Reasoning

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👁️ Fundamentals of visual etiology

Logical thinking through pictures and figures!

1️⃣ Types of visual etiology

Type	Explanation
Image sequence	Finding the next image
mirror image	Mirror Image Detection
Image of water	Water Image Detection
figure number	Triangle and square counting
Folding & Perforating	Paper folding and perforation
Find a single	Choose a different image

2️⃣ Mirror Image

Rule:Left-right changes, up-down doesn't change
Mirror right side → left side image

Characters:b↔d, p↔q, E↔Ǝ

3️⃣ Water Image

Rule:Up-down changes, left-right doesn't change
will be reversed

Characters:b↔p, d↔q, M↔W

4️⃣ Figure count

triangles	Count from smallest to largest
Squares	Count up to 1×1, 2×2, 3×3...
rectangles	Count the squares as well

5️⃣ Picture sequence rules

Rotation:Clockwise/Counterclockwise
Count:Addition/decrease
Color:White↔black transition
Location:Up↔down, left↔right movement

📐 Visual Causal Formulas

🔢 Figure count formulas

Figure	Formula (n×n grid)
Squares	n(n+1)(2n+1)/6
rectangles	n²(n+1)²/4
Triangles (step)	n(n+2)(2n+1)/8

🪞 Mirror Image Laws

Mirror space	Change
Right side	Left↔right will change
Left side	Left↔right will change
Top page	Change up↔down
Down side	Change up↔down

💧 Law of water image

Always:Up↔down changes, left-right doesn't change
The image will be reversed

🔄 Rotation angles

45° rotation	8 stages 1 round
90° rotation	4 stages 1 round
180° rotation	2 stages 1 round

📚 Solved Questions – 10

Question 1: Mirror image

What is the mirror image of the word HELP?

Solution:Left-right dynamic
HELP →PLƎH(Letters also rotate)

Question 2: Image of water

What is the water image of the word SWAN?

Solution:Up-down dynamic
S→S, W→M, A→∀, N→N =SM∀N

Question 3: Number of squares

How many total squares are there in a 3×3 grid?

Solution:n(n+1)(2n+1)/6 = 3×4×7/6 =14
(1×1=9, 2×2=4, 3×3=1)

Question 4: Number of rectangles

How many rectangles are there in a 2×3 grid?

Solution:m×n grid = m(m+1)×n(n+1)/4
= 2×3×3×4/4 =18

Question 5: Clockwise rotation

If the image rotates 90° clockwise?

Solution:Rotates to the right
Up→Right, Right→Down, Down→Left, Left→Up

Question 6: Anticlockwise

If the image rotates 90° counter-clockwise?

Solution:Rotates to the left
Up→Left, Left→Down, Down→Right, Right→Up

Question 7: Folding & Perforating

If paper is folded 2 times and punched 1?

Solution:2ⁿ holes if folded n times
2 times = 2² =4 holes

Question 8: 4×4 squares

How many total squares in a 4×4 grid?

Solution:4×5×9/6 =30
(1×1=16, 2×2=9, 3×3=4, 4×4=1)

Question 9: Number mirror

3:15 What time is the mirror image of the clock?

Solution:12:00 - Time = Glass Time
11:60 - 3:15 =8:45

Question 10: Triangle Count

How many triangles are there if a triangle is divided by 3 lines?

Solution:Count step by step
Add small + large and count

⚡ Speed shortcuts

🪞 Glass velocity law

Invariant characters:A, H, I, M, O, T, U, V, W, X, Y
Clock Time:11:60 - Time = Glass Time

💧 Law of velocity of water

Invariant characters:B, C, D, E, H, I, K, O, X
The image will only change upside down

🔢 To remember

2×2 squares	5
3×3 squares	14
4×4 squares	30
5×5 squares	55

📋 Folding rule

Fold n times + 1 hole = 2ⁿ holes
1 fold = 2, 2 fold = 4, 3 fold = 8

💡 Exam Tips

mirror = left↔right shift
Water = up↔downward change
Squares = 1²+2²+3²+...+n²
Find the cycle style first
Compare all 4 pictures to find the single one

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