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:

1. First circle:
- Top-left: 6
- Top-right: 4
- Bottom-left: 8
- Bottom-right: 6

2. Second circle:
- Top-left: 7
- Top-right: 8
- Bottom-left: 6
- Bottom-right: 7

3. Third circle:
- Top-left: 1
- Top-right: 3
- Bottom-left: 8
- Bottom-right: 4

4. Fourth circle:
- Top-left: 5
- Top-right: 5
- Bottom-left: 2
- Bottom-right: ? (we need to find this)

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Let’s look for a pattern across all circles. Perhaps there is a relationship between the numbers in the quadrants.

Let’s denote the positions:
- A = top-left
- B = top-right
- C = bottom-left
- D = bottom-right

So we have:

Circle 1: A=6, B=4, C=8, D=6
Circle 2: A=7, B=8, C=6, D=7
Circle 3: A=1, B=3, C=8, D=4
Circle 4: A=5, B=5, C=2, D=?

Now, let’s look for a possible mathematical relationship.

Try checking if A × B = C × D, or something similar.

Circle 1:

6 × 4 = 24
8 × 6 = 48 → Not equal.

Try A + B = C + D?
6 + 4 = 10
8 + 6 = 14 → No.

Try A + C = B + D?
6 + 8 = 14
4 + 6 = 10 → No.

Try A × C = B × D?
6 × 8 = 48
4 × 6 = 24 → No.

Wait — what if it's not multiplication, but something else?

Look at Circle 1:
Top: 6 and 4
Bottom: 8 and 6
Is there a relationship between top and bottom?

6 → 8? (increased by 2)
4 → 6? (increased by 2)
Yes! So maybe bottom row is top row + 2?

But check Circle 2:
Top: 7, 8
Bottom: 6, 7
7 → 6 (decreased by 1), 8 → 7 (decreased by 1) → So bottom = top - 1

Not consistent.

What about Circle 3:
Top: 1, 3
Bottom: 8, 4
No clear arithmetic shift.

Maybe try looking at sums or products of opposite numbers?

Try A × D vs B × C?

Circle 1:
A×D = 6×6 = 36
B×C = 4×8 = 32 → Not equal.

Try A + D vs B + C?

6+6 = 12
4+8 = 12 → Equal!

Oh! That’s interesting.

Circle 1:
A + D = 6 + 6 = 12
B + C = 4 + 8 = 12 → Same

Circle 2:
A + D = 7 + 7 = 14
B + C = 8 + 6 = 14 → Same!

Circle 3:
A + D = 1 + 4 = 5
B + C = 3 + 8 = 11 → Not equal.

Hmm, not matching.

Wait — maybe I made a mistake.

Circle 3:
A = 1, D = 4 → 1+4 = 5
B = 3, C = 8 → 3+8 = 11 → Not equal.

So that breaks the pattern.

Wait — perhaps another idea.

Let’s try A × B + C = D or some formula.

Try Circle 1:
6 × 4 = 24, then 24 / something?

Wait — maybe think differently.

Let’s look at diagonals.

In Circle 1:
Top-left = 6, Bottom-right = 6 → same
Top-right = 4, Bottom-left = 8 → different

But 6 and 6 are equal — so diagonal?

Wait — Circle 2: 7 and 7 → also equal diagonally?

Top-left = 7, Bottom-right = 7 → yes
Top-right = 8, Bottom-left = 6 → different

So in both Circle 1 and 2, top-left = bottom-right

Check Circle 3:
Top-left = 1, bottom-right = 4 → not equal

So no.

But wait — maybe sum of opposite corners?

Try A + D = B + C?

Circle 1:
A + D = 6 + 6 = 12
B + C = 4 + 8 = 12 → Yes

Circle 2:
A + D = 7 + 7 = 14
B + C = 8 + 6 = 14 → Yes

Circle 3:
A + D = 1 + 4 = 5
B + C = 3 + 8 = 11 → Not equal

Still not working.

Wait — maybe the product?

Circle 1:
A × D = 6 × 6 = 36
B × C = 4 × 8 = 32 → No

Circle 2:
7 × 7 = 49
8 × 6 = 48 → Close but not equal.

Not helpful.

Wait — perhaps look at sum of top and sum of bottom?

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

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

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

Not helping.

Alternative idea: Maybe the bottom-right number is determined by the other three?

Let’s suppose that D = A + B - C or something like that.

Try Circle 1:
D = 6 → Is 6 = 6 + 4 - 8 = 10 - 8 = 2? No
6 = 6 + 8 - 4 = 10? No

Try D = C - A + B?

6 = 8 - 6 + 4 = 6 → Yes!

So D = C - A + B?

Check: C = 8, A = 6, B = 4 → 8 - 6 + 4 = 6 → Yes

Now test Circle 2:
D = 7
C = 6, A = 7, B = 8
6 - 7 + 8 = 7 → Yes!

Now Circle 3:
D = 4
C = 8, A = 1, B = 3
8 - 1 + 3 = 10 → But D is 4 → No

Doesn't work.

Try D = A + B - C?

Circle 1: 6 + 4 - 8 = 2 ≠ 6 → No

Try D = C - B + A?

Circle 1: 8 - 4 + 6 = 10 → No

Wait — maybe D = A × B / C?

6 × 4 / 8 = 24/8 = 3 → No

Try D = (A + C) / (B / something) — too vague.

Another idea: Look at products or differences.

Wait — let's go back.

Notice in Circle 1:
6, 4
8, 6

See: 6 → 8 (up by 2), 4 → 6 (up by 2) — so bottom = top + 2?

But Circle 2:
7, 8 → 6, 7 → down by 1

Circle 3:
1, 3 → 8, 4 → not consistent

Wait — maybe look at 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 obvious pattern.

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

Circle 1: 6×4 = 24, 8×6 = 48 → No

Circle 2: 7×8 = 56, 6×7 = 42 → No

Circle 3: 1×3 = 3, 8×4 = 32 → No

No.

Wait — maybe the bottom-left number is related to the top-left and top-right?

Let’s look at Circle 1:
Top-left: 6, top-right: 4, bottom-left: 8
6 + 4 = 10 → not 8
6 × 4 = 24 → no

Wait — Circle 1: 6 and 4 → 8 and 6
Is 8 = 6 + 2, 6 = 4 + 2 → so bottom = top + 2?

Circle 2: 7 and 8 → 6 and 7
7 → 6 (-1), 8 → 7 (-1) → bottom = top - 1

Circle 3: 1 and 3 → 8 and 4
1 → 8 (+7), 3 → 4 (+1) — no pattern

But notice: In Circle 1 and Circle 2, the bottom row is shifted by a constant from the top row.

But Circle 3 doesn’t follow.

Wait — maybe the bottom-right number is derived from others?

Let’s try to see if there’s a pattern involving all circles.

Let’s list them again:

| Circle | A | B | C | D |
|--------|---|---|---|---|
| 1 | 6 | 4 | 8 | 6 |
| 2 | 7 | 8 | 6 | 7 |
| 3 | 1 | 3 | 8 | 4 |
| 4 | 5 | 5 | 2 | ? |

Now, look at A and D:
- Circle 1: A=6, D=6 → equal
- Circle 2: A=7, D=7 → equal
- Circle 3: A=1, D=4 → not equal
- Circle 4: A=5, D=? → maybe 5?

But in Circle 3, A=1, D=4 → not equal, so probably not.

But in Circles 1 and 2, A = D.

Is that a coincidence?

Wait — maybe A and D are equal only in first two?

But Circle 3 breaks it.

Wait — maybe A + B = C + D?

Circle 1: 6+4 = 10, 8+6 = 14 → No

Circle 2: 7+8=15, 6+7=13 → No

Circle 3: 1+3=4, 8+4=12 → No

No.

Wait — let’s try A × C = B × D?

Circle 1: 6×8 = 48, 4×6 = 24 → No

Circle 2: 7×6 = 42, 8×7 = 56 → No

Circle 3: 1×8 = 8, 3×4 = 12 → No

No.

Wait — how about (A + B) × (C + D)?

Too big.

Another idea: Maybe the number in the bottom-right is the average or something?

Wait — let’s look at Circle 3:
A=1, B=3, C=8, D=4

Is there any relation?

1 and 3 → 1+3=4 → D=4

Oh! A + B = D?

1 + 3 = 4 → Yes!

Check Circle 1: A+B = 6+4 = 10, D=6 → No

Circle 2: 7+8=15, D=7 → No

Only works for Circle 3.

Wait — Circle 1: A=6, B=4, C=8, D=6

Is D = C - 2? 8 - 2 = 6 → Yes

Circle 2: C=6, D=7 → 6 +1 =7 → D = C +1

Circle 3: C=8, D=4 → 8 - 4 =4 → D = C - 4

No pattern.

Wait — maybe D = A + C - B?

Circle 1: 6 + 8 - 4 = 10 → D=6 → No

Circle 2: 7 + 6 - 8 = 5 → D=7 → No

Circle 3: 1 + 8 - 3 = 6 → D=4 → No

No.

Wait — try D = B + C - A?

Circle 1: 4 + 8 - 6 = 6 → Yes! D=6

Circle 2: 8 + 6 - 7 = 7 → Yes! D=7

Circle 3: 3 + 8 - 1 = 10 → But D=4 → No

Wait — 10 ≠ 4

But almost — 3+8-1=10, but D=4

But wait — maybe D = (A + B + C) / something?

Circle 3: 1+3+8=12, 12/3=4 → D=4 → Yes!

Oh! So D = (A + B + C) / 3?

Check Circle 1: (6+4+8)/3 = 18/3 = 6 → D=6 → Yes!

Circle 2: (7+8+6)/3 = 21/3 = 7 → D=7 → Yes!

Circle 3: (1+3+8)/3 = 12/3 = 4 → D=4 → Yes!

Perfect!

So the rule is:
Bottom-right number = (Top-left + Top-right + Bottom-left) / 3

That is:
D = (A + B + C) / 3

Now apply to Circle 4:

A = 5, B = 5, C = 2

So D = (5 + 5 + 2) / 3 = 12 / 3 = 4

Therefore, the missing number is 4.

✔ Let’s verify:

- Circle 1: (6+4+8)/3 = 18/3 = 6 ✔️
- Circle 2: (7+8+6)/3 = 21/3 = 7 ✔️
- Circle 3: (1+3+8)/3 = 12/3 = 4 ✔️
- Circle 4: (5+5+2)/3 = 12/3 = 4 ✔️

Perfect!

✔ Final Answer: 4