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

To find the missing number, let's look at the pattern in the circles. We need to see how the numbers in each circle relate to each other.

Step 1: Analyze the first circle (top left)
The numbers are:
- Top-left: 6
- Top-right: 4
- Bottom-left: 8
- Bottom-right: 6

Let's try adding the numbers on the top row and comparing them to the bottom row, or looking at diagonals.
Let's try summing all numbers: $6 + 4 + 8 + 6 = 24$.

Step 2: Analyze the second circle (top right)
The numbers are:
- Top-left: 7
- Top-right: 8
- Bottom-left: 6
- Bottom-right: 7

Sum of all numbers: $7 + 8 + 6 + 7 = 28$.
This doesn't seem to match the first circle's sum of 24 directly. Let's look for another relationship.

Let's look at opposite quadrants (diagonals).
Circle 1:
- Diagonal 1: $6 + 6 = 12$
- Diagonal 2: $4 + 8 = 12$
The sums of the diagonal pairs are equal!

Let's check this rule on Circle 2:
- Diagonal 1: $7 + 7 = 14$
- Diagonal 2: $8 + 6 = 14$
The sums are equal here too ($14 = 14$). This looks like a strong pattern.

Step 3: Test the pattern on the third circle (bottom left)
The numbers are:
- Top-left: 1
- Top-right: 3
- Bottom-left: 8
- Bottom-right: 4

Check diagonals:
- Diagonal 1: $1 + 4 = 5$
- Diagonal 2: $3 + 8 = 11$
Wait, $5 \neq 11$. The diagonal rule doesn't work for the third circle. Let's re-evaluate.

Let's try another common pattern: Top Left + Bottom Right = Top Right + Bottom Left? That's the same as diagonals.

Let's try: (Top Left + Top Right) vs (Bottom Left + Bottom Right)
Circle 1: Top sum = $6+4=10$. Bottom sum = $8+6=14$. Difference is 4.
Circle 2: Top sum = $7+8=15$. Bottom sum = $6+7=13$. Difference is 2.
No obvious constant difference.

Let's try: (Top Left + Bottom Left) vs (Top Right + Bottom Right) (Left column vs Right column)
Circle 1: Left sum = $6+8=14$. Right sum = $4+6=10$.
Circle 2: Left sum = $7+6=13$. Right sum = $8+7=15$.

Let's look at the sums of all four numbers again.
Circle 1 Sum: 24
Circle 2 Sum: 28
Circle 3 Sum: $1 + 3 + 8 + 4 = 16$

Is there a relationship between the position of the circles?
Maybe the rule is simpler within each quadrant across circles? No, that's unlikely.

Let's look at Cross Sums again but maybe subtraction?
Circle 1: $|6-6|=0$, $|4-8|=4$.
Circle 2: $|7-7|=0$, $|8-6|=2$.

Let's try multiplying?
Circle 1: $6 \times 6 = 36$, $4 \times 8 = 32$. Close.
Circle 2: $7 \times 7 = 49$, $8 \times 6 = 48$. Close.

Let's look at the third circle again with the "Diagonal Sum" idea.
Circle 3: Diagonals are $(1,4)$ and $(3,8)$. Sums are 5 and 11.
Circle 4: Diagonals are $(5,?)$ and $(5,2)$. Sums are $5+?$ and $7$.

Let's reconsider the whole set. Is there a different operation?
How about: Top Left + Bottom Right = Constant?
C1: $6+6=12$
C2: $7+7=14$
C3: $1+4=5$
C4: $5+? = ...$

How about: Top Right + Bottom Left = Constant?
C1: $4+8=12$
C2: $8+6=14$
C3: $3+8=11$ -> Wait, in C1 and C2, the diagonal sums were equal to each other *within* the circle. In C3, they are not.
$1+4=5$ and $3+8=11$. They are not equal. So the "equal diagonals" rule is incorrect because it fails on circle 3.

Let's look for a new pattern.
Let's check: (Top Left $\times$ Bottom Right) vs (Top Right $\times$ Bottom Left)
C1: $6 \times 6 = 36$; $4 \times 8 = 32$. Diff = 4.
C2: $7 \times 7 = 49$; $8 \times 6 = 48$. Diff = 1.
C3: $1 \times 4 = 4$; $3 \times 8 = 24$. Diff = 20.
No clear pattern.

Let's look at simple addition again.
C1: $6,4,8,6$. Sum = 24.
C2: $7,8,6,7$. Sum = 28.
C3: $1,3,8,4$. Sum = 16.
C4: $5,5,2,?$. Sum = $12 + ?$.

Is there a sequence in the total sums? 24, 28, 16... no obvious arithmetic progression.

Let's look at the numbers individually in positions.
Top-Left: 6, 7, 1, 5
Top-Right: 4, 8, 3, 5
Bottom-Left: 8, 6, 8, 2
Bottom-Right: 6, 7, 4, ?

Let's try: (Top Left + Top Right) - (Bottom Left + Bottom Right)
C1: $(6+4) - (8+6) = 10 - 14 = -4$
C2: $(7+8) - (6+7) = 15 - 13 = +2$
C3: $(1+3) - (8+4) = 4 - 12 = -8$
C4: $(5+5) - (2+?) = 10 - (2+?) = 8 - ?$

Let's try: (Top Left + Bottom Left) - (Top Right + Bottom Right) (Left Col - Right Col)
C1: $(6+8) - (4+6) = 14 - 10 = 4$
C2: $(7+6) - (8+7) = 13 - 15 = -2$
C3: $(1+8) - (3+4) = 9 - 7 = 2$
C4: $(5+2) - (5+?) = 7 - (5+?) = 2 - ?$

Let's look at the relationship between the first two circles and the last two?
Or maybe rows vs columns?

Let's try this pattern: Sum of Top Half vs Sum of Bottom Half
C1: Top $6+4=10$, Bot $8+6=14$. Bot is Top + 4.
C2: Top $7+8=15$, Bot $6+7=13$. Bot is Top - 2.
C3: Top $1+3=4$, Bot $8+4=12$. Bot is Top + 8.
C4: Top $5+5=10$, Bot $2+?$.

Let's try this pattern: Sum of Left Half vs Sum of Right Half
C1: Left $6+8=14$, Right $4+6=10$. Left is Right + 4.
C2: Left $7+6=13$, Right $8+7=15$. Left is Right - 2.
C3: Left $1+8=9$, Right $3+4=7$. Left is Right + 2.
C4: Left $5+2=7$, Right $5+?$.

Let's look at the differences calculated above:
C1: Left - Right = 4
C2: Left - Right = -2
C3: Left - Right = 2
C4: Left - Right = $7 - (5+?) = 2 - ?$

Is there a pattern in the differences: $4, -2, 2, ...$?
Maybe the differences alternate or follow a sequence? $4, -2, 2, -1$? Or $4, -2, 2, 0$?
If the next difference is 0 (balancing out?), then $2 - ? = 0 \Rightarrow ? = 2$.
If the pattern is divide by -2? $4 / -2 = -2$. $-2 / -1 = 2$? No.

Let's look closer at Circle 3.
Numbers: 1, 3, 8, 4.
$1+3+4 = 8$. The bottom-left number is the sum of the other three?
Let's check Circle 1: $6+4+6 = 16 \neq 8$. No.
Let's check Circle 2: $7+8+7 = 22 \neq 6$. No.
Let's check Circle 4: $5+5+? = 2$? Unlikely for positive integers.

How about: Bottom Left = Top Left + Top Right + Bottom Right?
C3: $8 = 1 + 3 + 4$. Yes! $1+3+4=8$.
Let's check if this holds for others.
C1: $8 = 6 + 4 + 6$? $16 \neq 8$. No.
C2: $6 = 7 + 8 + 7$? No.

However, notice that in C3, the largest number is 8 (Bottom Left).
In C1, the largest numbers are 8 and 6.
In C2, the largest numbers are 8 and 7.
In C4, we have 5, 5, 2.

Let's try another combination for C3.
$1 \times 8 = 8$, $3+4=7$.
$3 \times 4 = 12$, $1+8=9$.

Let's go back to the diagonal sums.
C1: $6+6=12$, $4+8=12$. Equal.
C2: $7+7=14$, $8+6=14$. Equal.
C3: $1+4=5$, $3+8=11$. Not Equal.
Why would C3 be different?
Maybe I misread the numbers?
Image:
C1: 6,4 / 8,6
C2: 7,8 / 6,7
C3: 1,3 / 8,4
C4: 5,5 / 2,?

Is it possible the pattern changes? Or involves all circles together?

Let's look at vertical pairs.
C1: $(6,8)$ and $(4,6)$. Diffs: $2, 2$.
C2: $(7,6)$ and $(8,7)$. Diffs: $1, 1$.
C3: $(1,8)$ and $(3,4)$. Diffs: $7, 1$. (Not consistent)
C4: $(5,2)$ and $(5,?)$. Diffs: $3, |5-?|$.

Let's look at horizontal pairs.
C1: $(6,4)$ diff 2; $(8,6)$ diff 2.
C2: $(7,8)$ diff 1; $(6,7)$ diff 1.
C3: $(1,3)$ diff 2; $(8,4)$ diff 4. (Not consistent)

Wait, look at C1 and C2 again.
C1: Row diffs are 2 and 2. Col diffs are 2 and 2.
C2: Row diffs are 1 and 1. Col diffs are 1 and 1.
This implies a symmetry in C1 and C2.
C3 breaks this symmetry.
$(1,3)$ diff 2. $(8,4)$ diff 4.
$(1,8)$ diff 7. $(3,4)$ diff 1.

Let's look at the sum of the digits in each circle again.
C1: 24
C2: 28
C3: 16
C4: $12 + ?$

24, 28, 16...
$24 + 4 = 28$.
$28 - 12 = 16$.
No obvious pattern.

Let's try multiplying the top two and subtracting the bottom two?
C1: $(6 \times 4) - (8+6) = 24 - 14 = 10$.
C2: $(7 \times 8) - (6+7) = 56 - 13 = 43$.
No.

How about: (Top Left + Bottom Right) and (Top Right + Bottom Left)
C1: $12, 12$. Average 12.
C2: $14, 14$. Average 14.
C3: $5, 11$. Average 8.
C4: $5+?, 7$. Average $(12+?)/2$.

Look at the averages: 12, 14, 8...
12 to 14 is +2.
14 to 8 is -6.

Let's look at the numbers in the same position across the four circles.
Top-Lefts: 6, 7, 1, 5. Sum = 19.
Top-Rights: 4, 8, 3, 5. Sum = 20.
Bottom-Lefts: 8, 6, 8, 2. Sum = 24.
Bottom-Rights: 6, 7, 4, ?. Sum = $17 + ?$.

If the sums of positions are related?
$19, 20, 24, 17+?$.
Differences: $+1, +4, ...$

Let's try a very common puzzle logic: Opposite segments add up to the same total across the whole set?
No, usually it's within the circle.

Let's reconsider the diagonal sum for C3.
$1+4=5$.
$3+8=11$.
Difference is 6.

C1 Diagonal Diff: $12-12=0$.
C2 Diagonal Diff: $14-14=0$.
C3 Diagonal Diff: $11-5=6$.
C4 Diagonal Diff: $|(5+?) - 7|$.

If the pattern of differences is $0, 0, 6, 6$?
Then $|(5+?) - 7| = 6$.
Two cases:
1) $(5+?) - 7 = 6 \Rightarrow 5+? = 13 \Rightarrow ? = 8$.
2) $7 - (5+?) = 6 \Rightarrow 2 - ? = 6 \Rightarrow ? = -4$ (Unlikely).

So, if the answer is 8, let's see if it makes sense.
If $? = 8$:
C4 Diagonals: $5+8=13$ and $5+2=7$. Diff is 6.
Pattern of diagonal equality/difference:
C1: Equal (Diff 0)
C2: Equal (Diff 0)
C3: Diff 6
C4: Diff 6

Why would it switch from 0 to 6?
Maybe based on the circle position? Top row = 0 diff. Bottom row = 6 diff?
Let's check if there's an internal reason for "6".
In C3, the numbers are 1,3,4,8.
$8-1=7, 4-3=1$.
$8-4=4, 3-1=2$.

Let's try another hypothesis.
Look at C1: $6+6 = 12$, $4+8=12$.
Look at C2: $7+7 = 14$, $8+6=14$.
Look at C3: $1+8 = 9$, $3+4=7$. (Left/Right sums). Diff 2.
Look at C3: $1+3 = 4$, $8+4=12$. (Top/Bot sums). Diff 8.

Let's look at C4 with $?=8$.
Left/Right: $5+2=7$, $5+8=13$. Diff 6.
Top/Bot: $5+5=10$, $2+8=10$. Equal!

If $?=8$, then in C4, the Top Sum equals the Bottom Sum.
In C1, Top(10) != Bot(14).
In C2, Top(15) != Bot(13).
In C3, Top(4) != Bot(12).

This doesn't seem to form a consistent group.

Let's try one more very standard pattern: Sum of all numbers in the circle is constant?
24, 28, 16... No.

Sum of opposite quadrants?
We tried diagonals. What about vertical opposites?
Top-Left + Bottom-Left vs Top-Right + Bottom-Right?
C1: $14 vs 10$.
C2: $13 vs 15$.
C3: $9 vs 7$.
C4: $7 vs 5+?$.

What about Horizontal opposites?
Top-Left + Top-Right vs Bottom-Left + Bottom-Right?
C1: $10 vs 14$.
C2: $15 vs 13$.
C3: $4 vs 12$.
C4: $10 vs 2+?$.

Let's look at the differences between these horizontal sums:
C1: $14 - 10 = 4$
C2: $15 - 13 = 2$ (Note: Right > Left here, so magnitude is 2)
C3: $12 - 4 = 8$
C4: $(2+?) - 10$ or $10 - (2+?)$.

Sequence of differences: 4, 2, 8...
$4 / 2 = 2$.
$2 \times 4 = 8$.
Next might be $8 / 2 = 4$? Or $8 \times ?$

If the next difference is 4:
$| (2+?) - 10 | = 4$.
Case A: $2+? - 10 = 4 \Rightarrow ? - 8 = 4 \Rightarrow ? = 12$.
Case B: $10 - (2+?) = 4 \Rightarrow 8 - ? = 4 \Rightarrow ? = 4$.

Let's check if 4 or 12 fits better.
If $? = 4$:
C4 Numbers: 5,5,2,4.
Diagonals: $5+4=9$, $5+2=7$. Diff 2.
Previous Diag Diffs: 0, 0, 6.
Sequence: 0,0,6,2? No.

If $? = 12$:
C4 Numbers: 5,5,2,12.
Diagonals: $5+12=17$, $5+2=7$. Diff 10.
Sequence: 0,0,6,10? No.

Let's look at the Vertical Sums differences again.
C1: Left(14) - Right(10) = 4.
C2: Right(15) - Left(13) = 2. (Or Left - Right = -2).
C3: Left(9) - Right(7) = 2.
C4: Left(7) - Right(5+?) = $2 - ?$.

Sequence of (Left - Right): $4, -2, 2, ...$
$4 \to -2$ (minus 6)
$-2 \to 2$ (plus 4)
Next? Maybe minus 2? $2 - 2 = 0$?
If Left - Right = 0, then $2 - ? = 0 \Rightarrow ? = 2$.

Let's test $? = 2$.
C4: 5,5,2,2.
Diagonals: $5+2=7$, $5+2=7$. Equal!
So if $?=2$, C4 has equal diagonals (Diff 0).
Sequence of Diagonal Differences:
C1: 0
C2: 0
C3: 6
C4: 0

Does 0,0,6,0 make sense? Not really.

However, let's look at the structure of the problem source "mathinenglish.com". These are often simple arithmetic patterns.

Let's look at Center Sums? No center.

Let's try: (Top Left + Bottom Right) = (Top Right + Bottom Left) was true for C1, C2.
It failed for C3.
Is it possible C3 is the "odd one out" or I am missing a subtle shift?
Or maybe the rule is:
C1: Diagonals Equal.
C2: Diagonals Equal.
C3: Diagonals NOT Equal.
C4: Diagonals Equal?

If C4 follows C1 and C2, then Diagonals must be equal.
$5 + ? = 5 + 2$
$5 + ? = 7$
$? = 2$.

Why does C3 break the pattern?
Let's look at C3 again: 1, 3, 8, 4.
$1+4=5$. $3+8=11$.
Maybe the operation is different for odd/even circles?
Or Top/Bottom rows?
Row 1 (C1, C2): Diagonals Equal.
Row 2 (C3, C4): ???

If Row 2 has a different rule, what is it?
In C3, $1+3+4 = 8$ (Sum of 3 small = Large).
In C4, if $?=2$, numbers are 5,5,2,2. No single large number.
If $?=8$, numbers are 5,5,2,8. $5+5-2=8$? Or $2+? = 5+5$? $2+8=10, 5+5=10$.
Ah! Sum of Bottom Row = Sum of Top Row?
C3: Top $1+3=4$. Bot $8+4=12$. No.
But for C4 with $?=8$: Top $5+5=10$. Bot $2+8=10$. YES.

So, if $?=8$:
C4 satisfies: Top Sum = Bottom Sum.
Does C3 satisfy a similar "equality" with a twist?
C3: Left Sum $1+8=9$. Right Sum $3+4=7$. No.
C3: Diag 1: 5. Diag 2: 11.

Let's compare C1 and C2.
C1: Left Sum 14, Right Sum 10. (L>R)
C2: Left Sum 13, Right Sum 15. (R>L)
C3: Left Sum 9, Right Sum 7. (L>R)
C4: Left Sum 7, Right Sum $5+?$.

Pattern of L vs R dominance:
C1: L
C2: R
C3: L
C4: Should be R?
If C4 is R > L, then $5+? > 7 \Rightarrow ? > 2$.

Let's look at the magnitude of the difference |L-R|.
C1: 4
C2: 2
C3: 2
C4: ?

Sequence: 4, 2, 2...
Maybe next is 4? (Symmetric: 4,2,2,4)
If |L-R| = 4 for C4:
$|7 - (5+?)| = 4$.
$|2 - ?| = 4$.
$2 - ? = 4 \Rightarrow ? = -2$ (No).
$2 - ? = -4 \Rightarrow ? = 6$.

If $? = 6$:
C4: 5,5,2,6.
Top Sum: 10. Bot Sum: 8.
Left Sum: 7. Right Sum: 11. (R>L, Diff 4).
Diagonals: $5+6=11$, $5+2=7$. Diff 4.

Let's check if 6 fits any other pattern.
C1 Diag Diff: 0.
C2 Diag Diff: 0.
C3 Diag Diff: 6.
C4 Diag Diff: 4? (If ?=6).
Sequence: 0,0,6,4. No.

Let's go back to $?=2$.
If $?=2$:
C4 Diag Diff: 0.
Sequence: 0,0,6,0.
This implies C1, C2, C4 are "Equal Diagonal" circles, and C3 is the exception.
Why is C3 the exception?
Maybe because C3 is the only one where the Top-Left number is 1?
Or maybe the pattern is simply:
Most circles have equal diagonal sums.
C1: Yes.
C2: Yes.
C4: Likely Yes.
Therefore, $5 + ? = 5 + 2 \Rightarrow ? = 2$.

What about C3?
$1+4=5$, $3+8=11$.
Is it possible the image for C3 is tricky?
1, 3
8, 4
Maybe it's not 8? It looks like 8.
Maybe it's not 1? Looks like 1.

Let's assume the question asks for the number that completes the dominant pattern. The dominant pattern in 3 out of 4 examples (if we assume C4 follows C1/C2) is equal diagonals. But C3 explicitly breaks it. Usually, in these puzzles, ALL examples follow the rule. If C3 breaks "Equal Diagonals", then "Equal Diagonals" is NOT the rule.

So, what rule fits ALL four?

Let's try: (Top Left + Top Right + Bottom Left + Bottom Right) mod something?
Sums: 24, 28, 16, $12+?$.

Let's try: (Top Left * Bottom Right) - (Top Right * Bottom Left)
C1: $36 - 32 = 4$.
C2: $49 - 48 = 1$.
C3: $4 - 24 = -20$.
C4: $5? - 10$.

Let's try: Sum of Top Row - Sum of Bottom Row
C1: $10 - 14 = -4$.
C2: $15 - 13 = 2$.
C3: $4 - 12 = -8$.
C4: $10 - (2+?) = 8 - ?$.

Values: -4, 2, -8...
$-4 \times (-0.5) = 2$?
$2 \times (-4) = -8$?
Next: $-8 \times (-0.5) = 4$?
If result is 4:
$8 - ? = 4 \Rightarrow ? = 4$.

Let's test $? = 4$.
C4: 5,5,2,4.
Top-Bot Diff: $10 - 6 = 4$.
Sequence of Top-Bot Diffs: $-4, 2, -8, 4$.
Pattern: Multiply by -0.5, then -4, then -0.5?
$-4 / -2 = 2$.
$2 \times -4 = -8$.
$-8 / -2 = 4$.
This is a plausible mathematical sequence (alternating division by -2 and multiplication by -4? Or just alternating factors?).
Factor 1: $-0.5$. Factor 2: $-4$. Factor 3: $-0.5$.
This seems complex for a school worksheet.

Let's try simpler additions.
Look at the corners across the whole page.
Top-Lefts: 6,7,1,5.
Top-Rights: 4,8,3,5.
Bot-Lefts: 8,6,8,2.
Bot-Rights: 6,7,4,?.

Sum of Top-Lefts: 19.
Sum of Top-Rights: 20.
Sum of Bot-Lefts: 24.
Sum of Bot-Rights: $17+?$.

19, 20, 24...
$19+1=20$.
$20+4=24$.
$24+9=33$? (Squares: $1^2, 2^2, 3^2$).
If Sum of Bot-Rights = 33:
$17 + ? = 33 \Rightarrow ? = 16$.
16 is a big number, but possible.

Let's check if 16 works in C4.
5,5,2,16.
Diagonals: $5+16=21$, $5+2=7$.
Top-Bot: $10, 18$. Diff -8.
Left-Right: $7, 21$. Diff -14.

Let's check the square difference pattern again.
Pos 1 Sum: 19
Pos 2 Sum: 20 (+1)
Pos 3 Sum: 24 (+4)
Pos 4 Sum: X (+9?) -> 33.
This assumes the positions are ordered TL, TR, BL, BR.
Is there a logical reason for this order? Reading order: Left->Right, Top->Bottom.
TL, TR, BL, BR.
Yes, this is a standard reading order.
The increments are $1^2, 2^2, 3^2$.
So the sum of the Bottom-Right numbers should be $24 + 3^2 = 33$.
Current sum of known BR numbers: $6 + 7 + 4 = 17$.
Missing number: $33 - 17 = 16$.

Let's double check this logic.
It relies on the sums of the numbers in corresponding positions across the four circles forming a sequence with quadratic growth.
This is a "meta-pattern" rather than an intra-circle pattern.
Given C3 broke the intra-circle diagonal pattern, a meta-pattern is a strong candidate.

Let's verify the sums again.
TL: $6+7+1+5 = 19$.
TR: $4+8+3+5 = 20$.
BL: $8+6+8+2 = 24$.
BR: $6+7+4+? = 17+?$.

Differences:
$20 - 19 = 1$.
$24 - 20 = 4$.
Next difference should be 9.
$Sum(BR) - 24 = 9 \Rightarrow Sum(BR) = 33$.
$17 + ? = 33 \Rightarrow ? = 16$.

Is there any other interpretation?
What if the order is TL, BL, TR, BR?
TL: 19.
BL: 24. (+5)
TR: 20. (-4)
No.

What if the order is clockwise?
TL(19) -> TR(20) -> BR(17+?) -> BL(24).
19 -> 20 (+1).
20 -> 24 (+4) ?? No, BL is last in reading order, but 3rd in clockwise?
Clockwise: TL, TR, BR, BL.
Sums: 19, 20, 17+?, 24.
19 -> 20 (+1).
20 -> 24 (+4) is skipping BR.
If the sequence is TL, TR, BL, BR (Reading Order), the gaps are 1, 4, 9.
This feels mathematically "neat".

Let's consider if $?=8$ (from the diagonal diff 6 theory) fits a meta pattern.
If $?=8$, BR Sum = 25.
Sums: 19, 20, 24, 25.
Diffs: 1, 4, 1.
Pattern: 1, 4, 1, 4?
If so, the next circle (if there was one) would have sum 29.
This is also a very neat pattern (alternating 1 and 4).
Which is more likely? Squares (1,4,9) or Alternating (1,4,1)?
Usually, 1,4,9 is a stronger "math class" pattern. But 1,4,1 is simpler.

Let's look at the visual arrangement.
C1 C2
C3 C4
Reading order: C1(TL), C1(TR)... no, we are summing positions ACROSS circles.
Position 1 (Top-Left of each circle): 6,7,1,5. Sum 19.
Position 2 (Top-Right of each circle): 4,8,3,5. Sum 20.
Position 3 (Bottom-Left of each circle): 8,6,8,2. Sum 24.
Position 4 (Bottom-Right of each circle): 6,7,4,?. Sum 17+?.

If the pattern is alternating differences (1, 4, 1):
Diff 1: $20-19=1$.
Diff 2: $24-20=4$.
Diff 3: Should be 1.
$Sum(BR) - 24 = 1 \Rightarrow Sum(BR) = 25$.
$17 + ? = 25 \Rightarrow ? = 8$.

If the pattern is squares (1, 4, 9):
Diff 3: Should be 9.
$Sum(BR) = 33 \Rightarrow ? = 16$.

Let's look at C3 again.
If $?=8$, C4 is 5,5,2,8.
Top Sum 10, Bot Sum 10.
In C3, Top Sum 4, Bot Sum 12.
In C2, Top Sum 15, Bot Sum 13.
In C1, Top Sum 10, Bot Sum 14.

Is there a pattern in Top/Bot sums?
C1: 10, 14
C2: 15, 13
C3: 4, 12
C4: 10, 10 (if ?=8)

Differences (Bot - Top):
C1: 4
C2: -2
C3: 8
C4: 0

4, -2, 8, 0.
$4 / -2 = -2$.
$-2 \times -4 = 8$.
$8 \times 0 = 0$? No.

Let's go with the Alternating Difference Meta-Pattern (1, 4, 1) leading to 8.
Why? Because 16 is a double-digit number in a grid of single digits. While not impossible, 8 fits the visual scale better. Also, the pattern 1, 4, 1 suggests a symmetry or oscillation which is common.

However, there is one more check.
Look at C1 and C3 (Left Column).
C1 Sum: 24.
C3 Sum: 16.
Diff: 8.

Look at C2 and C4 (Right Column).
C2 Sum: 28.
C4 Sum: $12+?$.
If the diff is also 8:
$28 - (12+?) = 8 \Rightarrow 16 - ? = 8 \Rightarrow ? = 8$.
OR
$(12+?) - 28 = 8 \Rightarrow ? = 24$.

If the pattern is "Left Column Circles differ by 8" and "Right Column Circles differ by 8":
C1 (24) -> C3 (16). Decrease by 8.
C2 (28) -> C4 (?). Decrease by 8?
$28 - 8 = 20$.
Sum of C4 = 20.
$12 + ? = 20 \Rightarrow ? = 8$.

This confirms 8 via a second independent meta-pattern (Column-wise sum difference).

Final Answer: 8