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 have 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 (with missing number):
```
Top-left: 5
Top-right: 5
Bottom-left: 2
Bottom-right: ?
```

We are to find the missing number in the bottom-right of Circle 4.

---

Let’s look for a pattern across the circles.

Step 1: Check if there’s a mathematical relationship between the numbers.

Let’s consider possible operations involving the four numbers in each circle.

Try checking if the sums or products of opposite or adjacent numbers follow a pattern.

#### Try: Sum of opposite numbers

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

So both diagonals sum to 12.

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

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

Hmm, not matching.

Wait — maybe it’s not about diagonal sums?

But in first two circles, diagonals sum to same value, but third doesn't.

Wait — let's double-check Circle 3:
- Top-left: 1
- Bottom-right: 4 → 1 + 4 = 5
- Top-right: 3
- Bottom-left: 8 → 3 + 8 = 11 → not equal.

So not consistent.

Alternative idea: Maybe product?

Try products:

Circle 1:
- 6 × 6 = 36
- 4 × 8 = 32 → not equal.

No.

Another idea: Maybe top row and bottom row?

Or perhaps the sum of top row vs bottom row?

Try that:

Circle 1:
- Top: 6 + 4 = 10
- Bottom: 8 + 6 = 14 → not equal

Circle 2:
- Top: 7 + 8 = 15
- Bottom: 6 + 7 = 13 → not equal

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

Not helpful.

---

Alternate idea: Look at positions.

Let’s suppose there’s a rule based on the numbers around the circle.

Try looking at each position across the circles.

Let’s list all positions:

| Circle | TL | TR | BL | BR |
|--------|----|----|----|----|
| 1 | 6 | 4 | 8 | 6 |
| 2 | 7 | 8 | 6 | 7 |
| 3 | 1 | 3 | 8 | 4 |
| 4 | 5 | 5 | 2 | ? |

Now, look at TL + TR + BL + BR — total sum per circle:

- 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 obvious pattern.

But wait — maybe there’s a relationship between top and bottom rows?

Try this: Is BL = something from top?

Look at Circle 1:
- TL=6, TR=4, BL=8, BR=6
- Notice: BL = 8, which is 6+4 - 2? Not clear.

Wait — another idea: Check if BR is related to other three numbers.

Try for each circle: can we get BR from TL, TR, BL?

Let’s test:

Circle 1: TL=6, TR=4, BL=8 → BR=6
Is there a relation? 6 + 4 = 10, 8 + 6 = 14 — no.

What if we do: TL × TR = 6×4 = 24, BL × BR = 8×6 = 48 — not helpful.

Wait — go back to diagonal sums.

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

Circle 2:
- TL + BR = 7 + 7 = 14
- TR + BL = 8 + 6 = 14 → equal

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

But wait — maybe I made a mistake?

Wait — is it possible that in some circles, it's not the diagonals, but something else?

Alternatively, maybe the product?

Circle 1:
- TL × BR = 6 × 6 = 36
- TR × BL = 4 × 8 = 32 → not equal

No.

Wait — what if we look at difference?

Try: (TL + TR) vs (BL + BR)

Circle 1:
- Top: 6+4 = 10
- Bottom: 8+6 = 14 → difference 4

Circle 2:
- Top: 7+8 = 15
- Bottom: 6+7 = 13 → diff -2

No.

Another idea: Maybe BR = TL + TR - BL or something?

Test in Circle 1:
- TL=6, TR=4, BL=8 → 6+4-8 = 2 ≠ 6 → no

Try: BR = BL - (TL - TR)? 8 - (6-4) = 8-2 = 6 → yes!

That works for Circle 1.

Try Circle 2:
- TL=7, TR=8, BL=6
- BR = BL - (TL - TR) = 6 - (7 - 8) = 6 - (-1) = 7 → matches BR=7 ✔

Circle 3:
- TL=1, TR=3, BL=8
- BR = 8 - (1 - 3) = 8 - (-2) = 10 → but actual BR is 4 → ✘

Nope.

Wait — maybe reverse?

Try: BR = TL + TR - BL?

Circle 1: 6+4 - 8 = 2 ≠ 6 → no

Try: BR = BL + TR - TL?

Circle 1: 8 + 4 - 6 = 6 → yes! ✔

Circle 2: 6 + 8 - 7 = 7 → yes! ✔

Circle 3: 8 + 3 - 1 = 10 → but BR is 4 → no ✘

Still no.

Wait — maybe different formula.

Try: BR = (TL × TR) / BL?

Circle 1: (6×4)/8 = 24/8 = 3 ≠ 6 → no

Try: BR = (TL + BL) / something?

Another idea: Let's look at the sum of the top two numbers and bottom two numbers.

Circle 1:
- Top: 6+4=10
- Bottom: 8+6=14 → 14 - 10 = 4

Circle 2:
- Top: 7+8=15
- Bottom: 6+7=13 → 13 - 15 = -2

Circle 3:
- Top: 1+3=4
- Bottom: 8+4=12 → 12 - 4 = 8

No pattern.

Wait — maybe the product of top vs product of bottom?

Circle 1:
- Top: 6×4=24
- Bottom: 8×6=48 → 48 / 24 = 2

Circle 2:
- Top: 7×8=56
- Bottom: 6×7=42 → 42 / 56 = 0.75

No.

Wait — go back to diagonal sums.

We saw:
- Circle 1: TL + BR = 6+6 = 12; TR + BL = 4+8 = 12 → equal
- Circle 2: 7+7=14; 8+6=14 → equal
- Circle 3: 1+4=5; 3+8=11 → not equal

But wait — maybe it's not diagonal sums, but other pattern.

Wait — could it be that BR = TL + TR - BL?

Try Circle 1: 6+4-8 = 2 ≠ 6 → no

Try: BR = BL - (TR - TL)?

Circle 1: 8 - (4 - 6) = 8 - (-2) = 10 ≠ 6

No.

Wait — try (TL × BL) / TR?

Circle 1: (6×8)/4 = 48/4 = 12 → not 6

No.

Another idea: Perhaps the sum of all four numbers is constant?

No:
- C1: 6+4+8+6 = 24
- C2: 7+8+6+7 = 28
- C3: 1+3+8+4 = 16
- C4: 5+5+2+x = 12+x

No.

Wait — maybe the missing number is determined by a pattern across the circles, not within.

Let’s look at the bottom-right values:

- C1: 6
- C2: 7
- C3: 4
- C4: ?

And top-left: 6,7,1,5
Top-right: 4,8,3,5
Bottom-left: 8,6,8,2

Notice:

In C1 and C3, bottom-left is 8.
In C2, it's 6.
In C4, it's 2.

Not helpful.

Wait — look at C1 and C2 — they both have equal TL and BR:
- C1: TL=6, BR=6
- C2: TL=7, BR=7

So in these two, BR = TL.

C3: TL=1, BR=4 → not equal

C4: TL=5, BR=? — maybe BR=5?

But why would that be?

Is there a reason?

Wait — check if BR = TL in C1 and C2 — yes.

But not in C3.

Unless there's a condition.

Wait — in C1 and C2, TR ≠ BL, but in C3, TR=3, BL=8 → different.

But in C4, TR=5, BL=2 → different.

So maybe when TR ≠ BL, BR = TL?

But in C3, TR≠BL, but BR≠TL → so no.

Wait — another idea: What if the product of top-left and top-right equals product of bottom-left and bottom-right?

Try:

Circle 1:
- TL×TR = 6×4 = 24
- BL×BR = 8×6 = 48 → no

Circle 2:
- 7×8 = 56
- 6×7 = 42 → no

Circle 3:
- 1×3 = 3
- 8×4 = 32 → no

No.

Wait — try sum of top = sum of bottom?

C1: 6+4=10, 8+6=14 → no

C2: 7+8=15, 6+7=13 → no

C3: 1+3=4, 8+4=12 → no

No.

Wait — let's try a different approach.

Let me look at differences between positions.

Try: BR = (TL + BL) - TR?

Circle 1: (6+8)-4 = 10 → no

BR = (TR + BL) - TL?

(4+8)-6 = 6 → yes!

Circle 1: (TR + BL) - TL = (4+8)-6 = 6 → BR=6 ✔

Circle 2: (8+6)-7 = 7 → BR=7 ✔

Circle 3: (3+8)-1 = 10 → but BR=4 → no ✘

Wait — not working.

Wait — try: BR = (TL + TR) - BL?

C1: (6+4)-8 = 2 ≠ 6

No.

Wait — try: BR = BL - (TL - TR)?

C1: 8 - (6-4) = 8-2 = 6 → yes ✔

C2: 6 - (7-8) = 6 - (-1) = 7 → yes ✔

C3: 8 - (1-3) = 8 - (-2) = 10 → but BR=4 → no ✘

Same as before.

But wait — what if the formula changes?

Maybe only applies to first two?

But then C3 breaks it.

Wait — unless I misread C3.

Let me recheck C3:

C3:
- TL=1
- TR=3
- BL=8
- BR=4

If BR = BL - (TL - TR) = 8 - (1-3) = 8 - (-2) = 10 → not 4

But if BR = TL + TR - BL = 1+3-8 = -4 → no

Wait — try: BR = (TL × TR) / BL?

1×3 / 8 = 3/8 → no

Another idea: Maybe the sum of the top two numbers equals the sum of the bottom two numbers?

C1: 6+4=10, 8+6=14 → no

C2: 7+8=15, 6+7=13 → no

C3: 1+3=4, 8+4=12 → no

No.

Wait — maybe the product of the top numbers equals the product of the bottom numbers?

C1: 6×4=24, 8×6=48 → no

C2: 7×8=56, 6×7=42 → no

C3: 1×3=3, 8×4=32 → no

No.

Wait — here's a new idea: Look at C1 and C2 — both have TL = BR

C1: TL=6, BR=6
C2: TL=7, BR=7

C3: TL=1, BR=4 → not equal
C4: TL=5, BR=?

But in C3, BR=4 — not equal.

But notice: In C1 and C2, the top-right and bottom-left are different.

Wait — in C1: TR=4, BL=8
In C2: TR=8, BL=6

No commonality.

Wait — what if we look at sum of all numbers?

C1: 6+4+8+6 = 24
C2: 7+8+6+7 = 28
C3: 1+3+8+4 = 16
C4: 5+5+2+x = 12+x

No pattern.

Wait — perhaps the number in BR is related to the other three via a fixed operation.

Let’s assume that in each circle, the bottom-right is determined by a formula like:

BR = (TL + TR + BL) / k or something.

Try C1: (6+4+8) = 18 → 18/k = 6 → k=3 → so BR = (TL+TR+BL)/3?

C1: (6+4+8)/3 = 18/3 = 6 → yes ✔

C2: (7+8+6)/3 = 21/3 = 7 → yes ✔

C3: (1+3+8)/3 = 12/3 = 4 → yes! ✔

Oh! It works!

C3: (1+3+8)/3 = 12/3 = 4 → matches BR=4 ✔

Now C4:
- TL=5, TR=5, BL=2
- Sum = 5+5+2 = 12
- BR = 12 / 3 = 4

So missing number is 4

Let’s verify:

Circle 4:
- TL=5, TR=5, BL=2
- Sum = 12
- BR = 12 / 3 = 4

Yes!

So the pattern is:
> Bottom-right = (Top-left + Top-right + Bottom-left) / 3

It works for all four circles!

Final Answer: 4

✔ Solution: The missing number is 4.

Explanation:

In each circle, the bottom-right number is the average (sum divided by 3) of the other three numbers:
- (TL + TR + BL) ÷ 3 = BR

Verify:
- C1: (6+4+8)/3 = 18/3 = 6 ✔
- C2: (7+8+6)/3 = 21/3 = 7 ✔
- C3: (1+3+8)/3 = 12/3 = 4 ✔
- C4: (5+5+2)/3 = 12/3 = 4 ✔

So the answer is 4.