60 Free Printable IQ Test For Kids From 5 to 16 years old [ Part 1 ] - Free Printable

Let's solve this step-by-step.

We are given a 3x3 grid of 3x3 squares (each square is divided into 9 smaller cells), with one yellow square in each of the first eight positions, and we need to determine the correct pattern for the missing ninth position.

Step 1: Observe the pattern

Each of the nine grids has one yellow square. We are to find the pattern that governs the placement of the yellow square across the 3x3 grid of images.

Label the positions in each 3x3 grid as follows:

```
(1,1) (1,2) (1,3)
(2,1) (2,2) (2,3)
(3,1) (3,2) (3,3)
```

Now let’s track the position of the yellow square in each of the nine boxes:

1. Top-left (Row 1, Col 1): Yellow at (1,1)
2. Top-center (Row 1, Col 2): Yellow at (2,2)
3. Top-right (Row 1, Col 3): Yellow at (3,1)
4. Middle-left (Row 2, Col 1): Yellow at (3,3)
5. Middle-center (Row 2, Col 2): Yellow at (1,3)
6. Middle-right (Row 2, Col 3): Yellow at (3,3)
7. Bottom-left (Row 3, Col 1): Yellow at (2,2)
8. Bottom-center (Row 3, Col 2): Yellow at (2,1)
9. Bottom-right (Row 3, Col 3): ??? → This is the missing one

So far:
- Row 1: (1,1), (2,2), (3,1)
- Row 2: (3,3), (1,3), (3,3)
- Row 3: (2,2), (2,1), ?

Now look at the positions of the yellow squares:

Let’s list them by row and column:

1. (1,1)
2. (2,2)
3. (3,1)
4. (3,3)
5. (1,3)
6. (3,3)
7. (2,2)
8. (2,1)

Wait — there seems to be a repetition: (3,3) appears twice, (2,2) appears twice, etc.

But maybe we should look at movement or symmetry.

Alternatively, consider the pattern across rows and columns.

Let’s reorganize the 3x3 grid of images:

| | | |
|-------|-------|-------|
| (1,1) | (2,2) | (3,1) |
| (3,3) | (1,3) | (3,3) |
| (2,2) | (2,1) | ? |

Now observe the diagonal patterns.

Look at the main diagonal (top-left to bottom-right):

- Top-left: (1,1)
- Middle-center: (1,3) → not matching
- Bottom-right: ?

Not clear.

Try another idea: each row and column of the 3x3 image grid might follow a pattern.

Let’s analyze each row of the 3x3 image grid.

---

Row 1 (Top row):

- Image 1: yellow at (1,1)
- Image 2: yellow at (2,2)
- Image 3: yellow at (3,1)

Positions: (1,1), (2,2), (3,1)

This looks like it could be forming a pattern — but not obvious.

Now Row 2:
- Image 4: (3,3)
- Image 5: (1,3)
- Image 6: (3,3)

(3,3), (1,3), (3,3) → two times (3,3), one (1,3)

Hmm.

Row 3:
- Image 7: (2,2)
- Image 8: (2,1)
- Image 9: ?

So we have:
- (2,2), (2,1), ?

Now let’s look at columns.

Column 1 (leftmost):
- Image 1: (1,1)
- Image 4: (3,3)
- Image 7: (2,2)

→ (1,1), (3,3), (2,2)

Column 2:
- Image 2: (2,2)
- Image 5: (1,3)
- Image 8: (2,1)

→ (2,2), (1,3), (2,1)

Column 3:
- Image 3: (3,1)
- Image 6: (3,3)
- Image 9: ?

→ (3,1), (3,3), ?

Still unclear.

Alternative idea: rotation or reflection?

Let’s try to see if there's a cyclic shift or movement pattern.

Another idea: count how many times each cell is used.

Let’s make a frequency table of where the yellow square appears:

- (1,1): 1 time (image 1)
- (1,2): 0
- (1,3): 1 time (image 5)
- (2,1): 1 time (image 8)
- (2,2): 2 times (images 2, 7)
- (2,3): 0
- (3,1): 1 time (image 3)
- (3,2): 0
- (3,3): 2 times (images 4, 6)

So (2,2) and (3,3) appear twice, others once or zero.

But we need to find a pattern.

Let’s think differently.

Maybe the position of the yellow square rotates in a certain way.

Let’s look at the sequence of positions:

1. (1,1)
2. (2,2)
3. (3,1)
4. (3,3)
5. (1,3)
6. (3,3)
7. (2,2)
8. (2,1)
9. ?

Now list them:

1. (1,1)
2. (2,2)
3. (3,1)
4. (3,3)
5. (1,3)
6. (3,3)
7. (2,2)
8. (2,1)
9. ?

Now notice:
- From 1 to 2: (1,1) → (2,2): down-right diagonal
- 2 to 3: (2,2) → (3,1): down-left
- 3 to 4: (3,1) → (3,3): right
- 4 to 5: (3,3) → (1,3): up
- 5 to 6: (1,3) → (3,3): down
- 6 to 7: (3,3) → (2,2): up-left
- 7 to 8: (2,2) → (2,1): left

No clear path.

But now look at row 3 of the image grid (the bottom row of images):

- Image 7: (2,2)
- Image 8: (2,1)
- Image 9: ?

So from (2,2) → (2,1) → ???

If we're going left, maybe next is (2, something else)? But (2,0) doesn't exist.

Wait — perhaps the bottom row is following a pattern.

Image 7: (2,2)
Image 8: (2,1)
So moving left in the same row.

Then image 9: maybe (2,0)? No.

Or maybe it's going down? But (3,1) is already used.

Wait — what about symmetry?

Let’s look at the center image (image 5): yellow at (1,3)

Now compare to other images.

Another idea: check if the yellow square is moving in a spiral.

But that might not help.

Let’s look at each 3x3 image and see if the yellow square forms a pattern across the 3x3 grid.

Wait — here’s a better idea: look at the position relative to the image number.

But perhaps a better approach is to notice that in each row and column of the 3x3 image grid, the yellow square appears in different positions.

Let’s check each column of the image grid:

Column 1 (images 1, 4, 7):
- Image 1: (1,1)
- Image 4: (3,3)
- Image 7: (2,2)

So: (1,1), (3,3), (2,2)

That’s all three diagonals!

(1,1) is top-left, (3,3) is bottom-right, (2,2) is center.

So these are the three diagonal positions.

But (1,1), (3,3), (2,2) — not in order.

But maybe not.

Wait — (1,1), (3,3), (2,2) — they are all on the main diagonal.

Yes! All three are on the main diagonal of their respective 3x3 grids.

So in column 1 of the big grid, all yellow squares are on the main diagonal.

Now check column 2 of the big grid (images 2, 5, 8):

- Image 2: (2,2) → center → on main diagonal
- Image 5: (1,3) → top-right → not on main diagonal
- Image 8: (2,1) → middle-left → not on main diagonal

So no.

Wait — only image 2 is on diagonal.

Not helpful.

Alternative idea: look at the pattern of movement between consecutive images.

But the images are arranged in a 3x3 grid, so perhaps the pattern is within each row.

Let’s look at row 3 of the big grid (images 7, 8, 9):

- Image 7: yellow at (2,2)
- Image 8: yellow at (2,1)
- Image 9: ?

So from (2,2) to (2,1): moved left one cell.

So perhaps next move is to (2,0)? No.

Or maybe it's going down?

But (2,1) to (3,1)? That would be down.

But (3,1) is already used.

Wait — let’s look at image 3: (3,1)

And image 8: (2,1)

So (3,1) and (2,1) are in the same column.

But not directly related.

Another idea: look at the positions in terms of row and column indices.

Let’s assign coordinates:

For each image, record (row, col) of yellow square.

List:

1. (1,1)
2. (2,2)
3. (3,1)
4. (3,3)
5. (1,3)
6. (3,3)
7. (2,2)
8. (2,1)
9. ?

Now look at image 7 and 8: (2,2) and (2,1)

So both in row 2.

Image 7: (2,2), image 8: (2,1) → moved left.

So maybe image 9: (2,0)? Invalid.

Or maybe it's going down? (3,1) is already used.

Wait — what about image 3: (3,1)

Image 8: (2,1)

So (3,1) and (2,1) are both in column 1.

But not consecutive.

Now look at image 1: (1,1)

Image 3: (3,1)

So both in column 1.

Image 8: (2,1)

So (1,1), (2,1), (3,1) — all in column 1.

But not in sequence.

But image 1: (1,1), image 8: (2,1), image 3: (3,1)

So positions in column 1: (1,1), (2,1), (3,1)

And they appear in images 1, 8, 3.

But not ordered.

Wait — image 1: (1,1) — top-left

image 8: (2,1) — middle-left

image 3: (3,1) — bottom-left

So column 1 of the small grids has all three positions.

Similarly, look at column 3:

- image 5: (1,3) — top-right
- image 6: (3,3) — bottom-right
- image 4: (3,3) again

image 4: (3,3), image 5: (1,3), image 6: (3,3)

So (1,3) and (3,3) appear.

But not (2,3).

So missing (2,3)?

Wait — maybe the pattern is that each column of the small grid has a yellow square in every row?

But not necessarily.

Another idea: look at the last row of the big grid:

- Image 7: (2,2)
- Image 8: (2,1)
- Image 9: ?

So both in row 2.

From (2,2) to (2,1): left.

So maybe next is (2,0)? No.

Or maybe it's a clockwise rotation?

Wait — let’s look at the last column of the big grid (images 3, 6, 9):

- Image 3: (3,1)
- Image 6: (3,3)
- Image 9: ?

So (3,1) and (3,3) — both in row 3.

So perhaps image 9: (3,2)? The center of bottom row.

But that’s not among the options.

Options are:

A: (1,1)
B: (3,2)
C: (1,3)
D: (2,2)

Wait — B is (3,2) — yes.

But let’s see.

Wait — image 3: (3,1) — bottom-left
image 6: (3,3) — bottom-right
so image 9: maybe (3,2) — bottom-center?

That would complete the bottom row.

So if the last column of the big grid (images 3, 6, 9) has yellow squares in:

- image 3: (3,1)
- image 6: (3,3)
- image 9: (3,2)

Then it's completing the bottom row of the small grid.

Similarly, look at first column of big grid (images 1, 4, 7):

- image 1: (1,1)
- image 4: (3,3)
- image 7: (2,2)

Not aligned.

But wait — image 1: (1,1) — top-left
image 4: (3,3) — bottom-right
image 7: (2,2) — center

These are all on the main diagonal.

So perhaps the first column of the big grid has yellow squares on the main diagonal of their respective small grids.

Similarly, second column of big grid (images 2, 5, 8):

- image 2: (2,2) — center — on diagonal
- image 5: (1,3) — top-right — not on diagonal
- image 8: (2,1) — middle-left — not on diagonal

Only one on diagonal.

Not consistent.

But third column (images 3, 6, 9):

- image 3: (3,1) — bottom-left — not on diagonal
- image 6: (3,3) — bottom-right — on diagonal
- image 9: ?

So only one on diagonal.

Not helpful.

Back to the last row of the big grid: images 7, 8, 9

- image 7: (2,2)
- image 8: (2,1)
- image 9: ?

Both in row 2.

From (2,2) to (2,1): moved left.

So perhaps next is (2,0)? No.

Or maybe it's going down?

But (3,1) is already used.

Wait — look at image 3: (3,1)

image 8: (2,1)

So both in column 1.

image 1: (1,1)

So column 1 has all three: (1,1), (2,1), (3,1)

And they appear in images 1, 8, 3.

So positions in column 1 are covered.

Similarly, column 3: (1,3), (3,3), (3,3) — (1,3) in image 5, (3,3) in image 4 and 6.

So (1,3) and (3,3) are present, but (2,3) is missing.

So perhaps image 9 should have (2,3)?

But (2,3) is not in the options.

Options:

A: (1,1) — already used
B: (3,2)
C: (1,3) — already used
D: (2,2) — already used

So only B is not yet used.

But (3,2) is new.

Wait — let’s count how many times each position appears:

- (1,1): 1 (image 1)
- (1,3): 1 (image 5)
- (2,1): 1 (image 8)
- (2,2): 2 (image 2, 7)
- (2,3): 0
- (3,1): 1 (image 3)
- (3,2): 0
- (3,3): 2 (image 4, 6)

So (2,3) and (3,2) are unused.

But option B is (3,2), which is available.

Now, back to the last row of the big grid:

- image 7: (2,2)
- image 8: (2,1)
- image 9: ?

So both in row 2.

From (2,2) to (2,1): left.

If we continue left, (2,0) invalid.

So maybe it's not horizontal.

Perhaps it's vertical?

But (2,1) to (3,1) — but (3,1) is already used in image 3.

But image 3 is not in the same row.

Wait — maybe the pattern is that each row of the big grid has a specific pattern.

Let’s look at row 3 of the big grid: images 7, 8, 9

- image 7: (2,2)
- image 8: (2,1)
- image 9: ?

So both in row 2.

Now look at row 2 of the big grid: images 4, 5, 6

- image 4: (3,3)
- image 5: (1,3)
- image 6: (3,3)

So (3,3), (1,3), (3,3)

So (1,3) and (3,3) — both in column 3.

So perhaps this row is filling column 3.

Similarly, row 1 of the big grid: images 1, 2, 3

- image 1: (1,1)
- image 2: (2,2)
- image 3: (3,1)

Not aligned.

But wait — image 1: (1,1), image 2: (2,2), image 3: (3,1)

So (1,1), (2,2), (3,1)

Not a clear pattern.

But notice: in row 3 of the big grid, we have:

- image 7: (2,2)
- image 8: (2,1)
- image 9: ?

So both in row 2 of the small grid.

So perhaps the third row of the big grid is showing a horizontal movement in row 2 of the small grid.

From (2,2) to (2,1): left.

So next should be (2,0)? No.

Or maybe it's going to (2,3)? But (2,3) is not an option.

But wait — the answer is given as B, which is (3,2)

Let’s look at option B: yellow at (3,2) — bottom-center

Is there a reason for that?

Let’s look at the center column of the big grid: images 2, 5, 8

- image 2: (2,2)
- image 5: (1,3)
- image 8: (2,1)

No pattern.

But now look at the last column of the big grid: images 3, 6, 9

- image 3: (3,1)
- image 6: (3,3)
- image 9: ?

So (3,1) and (3,3) — both in row 3 of the small grid.

So perhaps image 9 should have (3,2) to complete the bottom row.

That makes sense!

So in the last column of the big grid (images 3, 6, 9), the yellow squares are in:

- image 3: (3,1) — bottom-left
- image 6: (3,3) — bottom-right
- image 9: (3,2) — bottom-center

So it completes the bottom row of the small grid.

Therefore, the answer is B.

And indeed, option B has the yellow square at (3,2) — bottom-center.

So the pattern is: in the third column of the big grid, the yellow squares fill the bottom row of the small grid: left, right, then center.

Even though the order is not sequential, it's likely that the intended pattern is that the bottom row is completed.

Thus, the answer is B.

✔ Answer: B