Printable math brain teasers, shape patterns and IQ puzzles for ... - Free Printable

Let's analyze the pattern in the given circles. Each circle is divided into four quadrants, with numbers placed in each quadrant. We are to find the missing number (marked with a question mark) in the bottom-right circle.

Here are the four circles:

---

Circle 1:
```
Top-left: 6
Top-right: 4
Bottom-left: 8
Bottom-right: 6
```

Circle 2:
```
Top-left: 7
Top-right: 8
Bottom-left: 6
Bottom-right: 7
```

Circle 3:
```
Top-left: 1
Top-right: 3
Bottom-left: 8
Bottom-right: 4
```

Circle 4 (missing value):
```
Top-left: 5
Top-right: 5
Bottom-left: 2
Bottom-right: ?
```

We need to find a consistent rule or pattern across all circles that relates the numbers in the quadrants.

Let’s look for patterns.

---

Step 1: Look for arithmetic relationships

Try checking if there's a relationship between the top and bottom numbers, or left and right.

Let’s examine Circle 1:
- Top: 6, 4 → sum = 10
- Bottom: 8, 6 → sum = 14
- Left: 6, 8 → sum = 14
- Right: 4, 6 → sum = 10

Interesting: left and right sums are equal? No: 14 vs 10.

Wait — let's check if there’s a multiplication or other operation.

Try:
Is there a relationship between top-left × something?

Alternatively, consider the sum of opposite quadrants.

In Circle 1:
- Top-left (6) + Bottom-right (6) = 12
- Top-right (4) + Bottom-left (8) = 12 → same!

So: Opposite corners sum to the same value.

Check Circle 2:
- Top-left (7) + Bottom-right (7) = 14
- Top-right (8) + Bottom-left (6) = 14 → same!

Yes! So this seems to be a pattern.

Now Circle 3:
- Top-left (1) + Bottom-right (4) = 5
- Top-right (3) + Bottom-left (8) = 11 → not equal!

Hmm, not matching.

Wait — maybe not opposite corners?

Wait: 1 + 4 = 5, 3 + 8 = 11 → not equal.

So that breaks the pattern.

But wait — perhaps it's not opposite corners?

Let’s try another idea.

Maybe the sum of top row equals sum of bottom row, or left column equals right column?

Circle 1:
- Top: 6 + 4 = 10
- Bottom: 8 + 6 = 14 → no
- Left: 6 + 8 = 14
- Right: 4 + 6 = 10 → no

Not equal.

But notice:
Left: 6+8=14
Right: 4+6=10 → not equal.

But earlier we saw that in Circle 1 and 2, opposite corners summed to same value.

Wait — Circle 3:
- Top-left: 1
- Bottom-right: 4 → sum = 5
- Top-right: 3
- Bottom-left: 8 → sum = 11 → not equal.

So not consistent.

Alternative idea: Maybe the product?

Try Circle 1:
- 6×6 = 36
- 4×8 = 32 → no

Or maybe some formula involving all four numbers.

Let’s think differently.

Another common type of puzzle: the sum of the top two numbers equals the sum of the bottom two, or something like that.

Try:

Circle 1:
- Top: 6 + 4 = 10
- Bottom: 8 + 6 = 14 → no

Circle 2:
- Top: 7 + 8 = 15
- Bottom: 6 + 7 = 13 → no

Circle 3:
- Top: 1 + 3 = 4
- Bottom: 8 + 4 = 12 → no

No.

What about top-left × bottom-right = top-right × bottom-left?

That would be a diagonal product equality.

Try Circle 1:
- 6 × 6 = 36
- 4 × 8 = 32 → no

Circle 2:
- 7 × 7 = 49
- 8 × 6 = 48 → close but not equal

Circle 3:
- 1 × 4 = 4
- 3 × 8 = 24 → no

No.

Wait — what if it's top-left + top-right = bottom-left + bottom-right?

Try:

Circle 1:
- Top: 6 + 4 = 10
- Bottom: 8 + 6 = 14 → no

Circle 2:
- 7 + 8 = 15
- 6 + 7 = 13 → no

Circle 3:
- 1 + 3 = 4
- 8 + 4 = 12 → no

No.

Wait — maybe it's top-left + bottom-right = top-right + bottom-left?

That’s the opposite corners sum again.

Try:

Circle 1:
- 6 + 6 = 12
- 4 + 8 = 12 → yes!

Circle 2:
- 7 + 7 = 14
- 8 + 6 = 14 → yes!

Circle 3:
- 1 + 4 = 5
- 3 + 8 = 11 → no → 5 ≠ 11

But wait — that doesn’t work.

Unless I made a mistake.

Wait — in Circle 3:
- Top-left: 1
- Bottom-right: 4 → sum = 5
- Top-right: 3
- Bottom-left: 8 → sum = 11 → not equal.

So not consistent.

But Circle 1 and 2 follow the rule: diagonals sum to same value.

Circle 3 does not.

Wait — unless I misread the positions.

Let me double-check the layout.

Each circle has:
- Top-left, Top-right
- Bottom-left, Bottom-right

So in Circle 3:
- TL: 1
- TR: 3
- BL: 8
- BR: 4

So diagonals:
- TL + BR = 1 + 4 = 5
- TR + BL = 3 + 8 = 11 → not equal

So not the same.

But Circle 1 and 2 do satisfy it.

Maybe it's a different rule.

Let’s try sum of all four numbers?

Circle 1: 6+4+8+6 = 24
Circle 2: 7+8+6+7 = 28
Circle 3: 1+3+8+4 = 16
Circle 4: 5+5+2+? = 12 + ?

No clear pattern.

Try product? Unlikely.

Another idea: maybe the bottom-right is derived from others.

Look at Circle 1:
- TL: 6, TR: 4, BL: 8, BR: 6

Is BR related to others?

6 = ? Try: 6 = (6+4)/something? 10/1.66… no.

Notice: 6 (TL) and 6 (BR) are equal.

In Circle 2: 7 and 7 — TL and BR both 7.

In Circle 3: TL=1, BR=4 → not equal.

In Circle 4: TL=5, BR=? → could be 5?

But in Circle 3, it’s not.

But wait — in Circle 1 and 2, top-left = bottom-right

- Circle 1: 6 = 6 → yes
- Circle 2: 7 = 7 → yes
- Circle 3: 1 ≠ 4 → no
- Circle 4: 5 = ? → maybe 5?

But Circle 3 breaks it.

Unless there's a different rule.

Wait — maybe top-left + top-right = bottom-left + bottom-right?

Try:

Circle 1:
- 6 + 4 = 10
- 8 + 6 = 14 → no

No.

Wait — what if we look at columns?

Left column: TL + BL
Right column: TR + BR

Circle 1:
- Left: 6 + 8 = 14
- Right: 4 + 6 = 10 → no

Circle 2:
- Left: 7 + 6 = 13
- Right: 8 + 7 = 15 → no

Circle 3:
- Left: 1 + 8 = 9
- Right: 3 + 4 = 7 → no

No.

Another idea: difference between top and bottom?

Try:

Circle 1:
- TL - BL = 6 - 8 = -2
- TR - BR = 4 - 6 = -2 → same!

Oh! Both differences are -2.

Circle 2:
- TL - BL = 7 - 6 = 1
- TR - BR = 8 - 7 = 1 → same!

Circle 3:
- TL - BL = 1 - 8 = -7
- TR - BR = 3 - 4 = -1 → not equal

No.

But wait — in Circle 3: 1 - 8 = -7, 3 - 4 = -1 → not same.

But in Circle 1 and 2, top minus bottom gives same value for both columns.

So perhaps that’s the pattern?

But fails in Circle 3.

Wait — maybe top-left × bottom-right = top-right × bottom-left?

Try:

Circle 1:
- 6 × 6 = 36
- 4 × 8 = 32 → no

Circle 2:
- 7 × 7 = 49
- 8 × 6 = 48 → close, but not equal

Circle 3:
- 1 × 4 = 4
- 3 × 8 = 24 → no

No.

Wait — let’s go back.

Earlier we saw:

In Circle 1: TL + BR = 6 + 6 = 12; TR + BL = 4 + 8 = 12 → equal

In Circle 2: 7 + 7 = 14; 8 + 6 = 14 → equal

In Circle 3: 1 + 4 = 5; 3 + 8 = 11 → not equal

But maybe I have the positions wrong?

Wait — is it possible that the sum of the two diagonals is the same?

Yes, in Circle 1 and 2, yes.

But in Circle 3, it’s not.

Unless there’s a typo, or perhaps a different rule.

Wait — maybe it's top-left × top-right = bottom-left × bottom-right?

Try:

Circle 1: 6×4 = 24; 8×6 = 48 → no

Circle 2: 7×8 = 56; 6×7 = 42 → no

No.

Another idea: maybe the number in bottom-right is determined by the others via a formula.

Let’s suppose the rule is:

Bottom-right = (top-left + top-right + bottom-left) / something

Try Circle 1:
- (6 + 4 + 8) = 18 → 18 / ? = 6 → 18 / 3 = 6 → so divide by 3?

But in Circle 2: (7 + 8 + 6) = 21 → 21 / 3 = 7 → matches BR = 7

Circle 3: (1 + 3 + 8) = 12 → 12 / 3 = 4 → and BR = 4 → YES!

Oh! It works!

So the pattern is:

> Bottom-right = (Top-left + Top-right + Bottom-left) / 3

Let’s verify:

Circle 1:
- (6 + 4 + 8) = 18 → 18 / 3 = 6 → matches BR = 6 ✔

Circle 2:
- (7 + 8 + 6) = 21 → 21 / 3 = 7 → matches BR = 7 ✔

Circle 3:
- (1 + 3 + 8) = 12 → 12 / 3 = 4 → matches BR = 4 ✔

Perfect!

Now apply to Circle 4:

- Top-left = 5
- Top-right = 5
- Bottom-left = 2
- Bottom-right = ?

So:

(5 + 5 + 2) = 12 → 12 / 3 = 4

Therefore, ? = 4

✔

Final Answer: 4

---

Explanation:

The rule is:
The bottom-right number is the average of the top-left, top-right, and bottom-left numbers.

That is:
> Bottom-right = (Top-left + Top-right + Bottom-left) ÷ 3

This holds true for all three complete circles.

Applying it to the fourth circle:
> (5 + 5 + 2) ÷ 3 = 12 ÷ 3 = 4

Thus, the missing number is 4.