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

Explanation:
We are given four circles, each divided into four quadrants with numbers. The goal is to find the missing number in the bottom-right circle (the one with a question mark).

Let’s label each circle as a 2×2 grid:

Circle 1 (top-left):
- Top-left: 6
- Top-right: 4
- Bottom-left: 8
- Bottom-right: 6

Circle 2 (top-right):
- Top-left: 7
- Top-right: 8
- Bottom-left: 6
- Bottom-right: 7

Circle 3 (bottom-left):
- Top-left: 1
- Top-right: 3
- Bottom-left: 8
- Bottom-right: 4

Circle 4 (bottom-right):
- Top-left: 5
- Top-right: 5
- Bottom-left: 2
- Bottom-right: ?

Let’s look for a pattern.

Try checking sums of opposite corners:

- Circle 1:
Top-left + Bottom-right = 6 + 6 = 12
Top-right + Bottom-left = 4 + 8 = 12
→ Equal! ✔

- Circle 2:
Top-left + Bottom-right = 7 + 7 = 14
Top-right + Bottom-left = 8 + 6 = 14
→ Equal! ✔

- Circle 3:
Top-left + Bottom-right = 1 + 4 = 5
Top-right + Bottom-left = 3 + 8 = 11
→ Not equal ✘

Hmm — maybe not that.

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
No obvious pattern.

Try difference between top and bottom rows:

Circle 1:
Top row: 6 + 4 = 10
Bottom row: 8 + 6 = 14
Difference = 4

Circle 2:
Top: 7 + 8 = 15
Bottom: 6 + 7 = 13
Difference = –2

Not consistent.

Try product of diagonals?

Circle 1:
TL × BR = 6 × 6 = 36
TR × BL = 4 × 8 = 32 → no

Another idea: maybe each circle follows:
Top-left + Top-right = Bottom-left + Bottom-right?
Check:

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

What about:
Top-left + Bottom-left = Top-right + Bottom-right?
That’s left column sum = right column sum.

Circle 1: 6 + 8 = 14; 4 + 6 = 10 → no
Circle 2: 7 + 6 = 13; 8 + 7 = 15 → no
Circle 3: 1 + 8 = 9; 3 + 4 = 7 → no

Try another angle: maybe each circle has a rule like:
Bottom-right = (Top-left + Top-right) − Bottom-left?
Test:

Circle 1: (6 + 4) − 8 = 10 − 8 = 2 ≠ 6 → no
Circle 2: (7 + 8) − 6 = 9 ≠ 7 → no
Circle 3: (1 + 3) − 8 = –4 ≠ 4 → no

Try: Bottom-right = (Bottom-left + Top-right) − Top-left
Circle 1: (8 + 4) − 6 = 6 → YES!
Circle 2: (6 + 8) − 7 = 7 → YES!
Circle 3: (8 + 3) − 1 = 10 ≠ 4 → no

Wait — circle 3 fails.

Let’s double-check circle 3:
Numbers: 1 (TL), 3 (TR), 8 (BL), 4 (BR)

Maybe it's: Top-left × Bottom-right = Top-right × Bottom-left?
Circle 1: 6 × 6 = 36; 4 × 8 = 32 → no
Circle 2: 7 × 7 = 49; 8 × 6 = 48 → close but no
Circle 3: 1 × 4 = 4; 3 × 8 = 24 → no

Let’s list all numbers again carefully:

Circle 1:
6 4
8 6

Circle 2:
7 8
6 7

Circle 3:
1 3
8 4

Circle 4:
5 5
2 ?

Now look at differences between top-left and bottom-right:

C1: 6 → 6 → diff 0
C2: 7 → 7 → diff 0
C3: 1 → 4 → diff +3
C4: 5 → ? → ?

Top-right and bottom-left:

C1: 4 and 8 → diff −4
C2: 8 and 6 → diff +2
C3: 3 and 8 → diff −5
No.

Wait — what if we consider sum of top row equals sum of bottom row minus 2?
C1: top = 10, bottom = 14 → 14 − 10 = 4
C2: top = 15, bottom = 13 → 13 − 15 = −2
No.

Let me try a new approach: maybe each circle satisfies:
(Top-left + Bottom-right) = (Top-right + Bottom-left) − k, but k varies.

Alternatively, could it be about even/odd or digit patterns? Unlikely.

Let’s compute for each circle the value:
Bottom-right = |Top-left − Top-right| + Bottom-left?
C1: |6−4| + 8 = 2 + 8 = 10 ≠ 6
No.

Try: Bottom-right = Bottom-left − (Top-right − Top-left)
C1: 8 − (4 − 6) = 8 − (−2) = 10 ≠ 6
C2: 6 − (8 − 7) = 6 − 1 = 5 ≠ 7

Wait — look again at circles 1 and 2. They are symmetric in a way:

Circle 1:
6 4
8 6
→ TL = BR = 6
→ TR = 4, BL = 8 → not equal, but 4 + 8 = 12, and 6 + 6 = 12

Ah! Earlier I saw: TL + BR = TR + BL
C1: 6+6 = 12, 4+8 = 12 ✔
C2: 7+7 = 14, 8+6 = 14 ✔
Now check C3: TL + BR = 1 + 4 = 5; TR + BL = 3 + 8 = 11 → not equal.

But maybe C3 is a red herring? Or maybe I misread C3.

Wait — could the numbers be read differently? Let me re-express all circles as matrices:

C1:
[6, 4]
[8, 6]

C2:
[7, 8]
[6, 7]

C3:
[1, 3]
[8, 4]

C4:
[5, 5]
[2, ?]

Now compute TL + BR and TR + BL again:

C1: 6+6=12, 4+8=12 ✔
C2: 7+7=14, 8+6=14 ✔
C3: 1+4=5, 3+8=11 ✘
Unless… is there a typo? But we must work with given.

Maybe the rule is: TL + BR = constant per pair of circles? C1 and C2 both have TL = BR, i.e., diagonal symmetry.

In C1: TL = BR = 6
In C2: TL = BR = 7
In C4: TL = 5, so maybe BR = 5? That would make sense — mirror the pattern.

Check C3: TL = 1, BR = 4 → not equal. But maybe C3 is different — let’s see if any other relation holds for C3 that also fits C1, C2, and can predict C4.

Try: (TL × BR) − (TR × BL) = constant?

C1: 6×6 − 4×8 = 36 − 32 = 4
C2: 7×7 − 8×6 = 49 − 48 = 1
C3: 1×4 − 3×8 = 4 − 24 = −20
No.

What if we look at row sums:

C1: row1 = 10, row2 = 14 → difference = 4
C2: row1 = 15, row2 = 13 → diff = −2
C3: row1 = 4, row2 = 12 → diff = −8
Differences: 4, −2, −8 — decreasing by 6, then 6? Next would be −14? Then row2 − row1 = −14 → row2 = row1 −14. For C4: row1 = 5+5 = 10, so row2 = 10 −14 = −4 → but bottom row is 2 + ? = −4 → ? = −6. Unlikely for this level.

Let’s try a simpler idea: maybe each circle’s numbers add to a multiple of 4 or something.

C1 total = 24
C2 = 28
C3 = 16
Differences: +4, −12 — no.

Wait — what if the rule is:
Bottom-right = (Top-left + Bottom-left) − Top-right

Test:
C1: (6 + 8) − 4 = 10 ≠ 6
C2: (7 + 6) − 8 = 5 ≠ 7
C3: (1 + 8) − 3 = 6 ≠ 4

Reverse: Bottom-right = (Top-right + Bottom-left) − Top-left
C1: (4 + 8) − 6 = 6 ✔
C2: (8 + 6) − 7 = 7 ✔
C3: (3 + 8) − 1 = 10 ≠ 4 ✘

But C3 doesn’t fit. Could it be that C3 is meant to help us see another pattern? Let's compute what value would make C3 satisfy that rule:
We want: BR = (TR + BL) − TL = (3 + 8) − 1 = 10. But actual BR is 4. So maybe C3 uses a different rule — or perhaps I mis-copied.

Wait — maybe the circles are paired: C1 and C2 follow one rule, C3 and C4 follow another.

Look at C3:
1 3
8 4

What is 1 + 8 = 9, 3 + 4 = 7
9 − 7 = 2
C1: 6+8=14, 4+6=10, diff=4
C2: 7+6=13, 8+7=15, diff=−2
No.

Try multiplication of outer vs inner? Not helpful.

Let me search online-style pattern: often in such puzzles, the rule is:
Top-left × Bottom-right = Top-right × Bottom-left
We saw it’s almost true:
C1: 6×6 = 36, 4×8 = 32 → off by 4
C2: 7×7 = 49, 8×6 = 48 → off by 1
C3: 1×4 = 4, 3×8 = 24 → off by 20

Not it.

Wait — what if we consider digits: 6,4,8,6 — all even.
7,8,6,7 — mixed.
1,3,8,4 — two odd, two even.
5,5,2,? — two odd, one even, so ? likely even.

Try assuming the rule is: Bottom-right = Top-left for circles 1 and 2, so maybe for circle 4, since top-left = 5, answer = 5.

Does that fit any logic? C1: TL=6, BR=6
C2: TL=7, BR=7
C4: TL=5 → BR=5
C3 is the odd one out: TL=1, BR=4 — maybe a distractor, or maybe there's a second rule.

But why would C3 be there then? Perhaps the real rule is:
The two diagonals have the same sum — which works for C1 and C2, and if we enforce it on C3, BR should be 10, but it's 4, so maybe the image has a mistake? Unlikely.

Let me recalculate C3 carefully: top-left 1, top-right 3, bottom-left 8, bottom-right 4. Is it possible that the bottom-left is 2 instead of 8? No, we must use given.

Alternative insight: Maybe each circle satisfies:
Product of top row = sum of bottom row?

C1: 6×4 = 24; 8+6 = 14 → no
C2: 7×8 = 56; 6+7 = 13 → no

What about: (Top-left + Top-right + Bottom-left) mod 10 = Bottom-right?

C1: 6+4+8 = 18 → 8 ≠ 6
C2: 7+8+6 = 21 → 1 ≠ 7
No.

Let’s list all bottom-right values: 6, 7, 4, ?
Top-left: 6, 7, 1, 5
Bottom-left: 8, 6, 8, 2
Top-right: 4, 8, 3, 5

Notice in C1: BL = 8, TR = 4 → BL = 2 × TR
C2: BL = 6, TR = 8 → no
C3: BL = 8, TR = 3 → no
C4: BL = 2, TR = 5

Wait — in C1: TL = 6, BR = 6 → same
C2: TL = 7, BR = 7 → same
So likely, the pattern is TL = BR, and C3 is an exception or test of attention.

But why include C3 then? Maybe the rule is: If TL and BR are equal, then TR + BL = 2×TL
C1: TR+BL = 4+8=12 = 2×6 ✔
C2: 8+6=14 = 2×7 ✔
So rule:
- TL = BR
- TR + BL = 2 × TL

Now apply to C4: TL = 5, so BR should be 5, and TR + BL should be 2×5 = 10.
Given TR = 5, BL = 2 → 5 + 2 = 7 ≠ 10. Hmm, doesn’t satisfy.

Unless the rule is only TL = BR, and the sum condition is derived, not required.

Given that two out of three circles (C1, C2) have TL = BR, and C4 has TL = 5, most natural guess is BR = 5.

Also, in C3, TL = 1, BR = 4 — maybe it's a different case where TL + BR = 5, and TR + BL = 11 — no.

Let me try one last idea: compute (TL + TR) − (BL − BR)

C1: (6+4) − (8−6) = 10 − 2 = 8 — not helpful.

Wait — what if the missing number is 8? Let's test if any rule gives 8:

Assume BR = 8. Then C4: 5,5 / 2,8
Check TL + BR = 5+8=13
TR + BL = 5+2=7 — no.

BR = 3: 5+3=8, 5+2=7
BR = 4: 5+4=9, 5+2=7
BR = 6: 11 vs 7
Only when BR = 5 do we get TL = BR, which matches first two circles.

Given that standardized puzzles like this often use the simplest repeating pattern, and circles 1 and 2 clearly have TL = BR, it's very likely the intended rule is: bottom-right equals top-left.

Thus for circle 4: top-left is 5, so bottom-right is 5.

I will go with 5.

Final Answer: 5