find the missing number math puzzle game | vPuzzles - Free Printable

Let's solve this math puzzle step by step.

We are given three cross-shaped figures, each with a central square and four surrounding circles (top, bottom, left, right). The goal is to find the missing number in the center of the second cross (marked with a red question mark).

Here’s how the layout looks:

---

First Cross:
```
7
4 3 10
13
```

Second Cross:
```
9
5 ? 13
17
```

Third Cross:
```
9
2 7 16
23
```

We need to find a pattern that relates the numbers around the center to the center number.

Let’s analyze the first cross:
- Top: 7
- Left: 4
- Right: 10
- Bottom: 13
- Center: 3

Try to see if there’s a relationship between these numbers and the center.

Let’s try some operations.

One idea: Maybe the center number is related to the sum or difference of the surrounding numbers.

Try:
Top + Bottom = 7 + 13 = 20
Left + Right = 4 + 10 = 14
Not obviously related to 3.

Try:
(Left + Right) - (Top + Bottom) = (4+10) - (7+13) = 14 - 20 = -6 → not helpful.

Alternatively, think about sums of opposite pairs.

Try:
Top + Bottom = 7 + 13 = 20
Left + Right = 4 + 10 = 14
No direct link to 3.

Wait — maybe it's not arithmetic, but something else.

Let’s look at the third cross, which has known values.

Third cross:
- Top: 9
- Left: 2
- Right: 16
- Bottom: 23
- Center: 7

Try to find a pattern here.

Let’s suppose the center number is derived from the surrounding numbers via a formula.

Try this idea:
Maybe center = (Top + Bottom) - (Left + Right)?

Check third cross:
- (9 + 23) = 32
- (2 + 16) = 18
- 32 - 18 = 14 ≠ 7 → no

What if:
(Top + Left + Right + Bottom) / something = center?

Sum of all outer numbers in third cross: 9 + 2 + 16 + 23 = 50
50 / 7 ≈ 7.14 → not helpful.

Another idea: Maybe center = (Top × something) or similar.

Let’s look at differences.

Try:
Bottom - Top = 23 - 9 = 14
Right - Left = 16 - 2 = 14 → interesting! Both differences are 14.

Now check first cross:
- Bottom - Top = 13 - 7 = 6
- Right - Left = 10 - 4 = 6 → also equal!

Oh! That's promising.

So in both first and third crosses:
- Bottom - Top = Right - Left

Let’s verify:

First cross:
- Bottom - Top = 13 - 7 = 6
- Right - Left = 10 - 4 = 6 → same

Third cross:
- Bottom - Top = 23 - 9 = 14
- Right - Left = 16 - 2 = 14 → same

So this pattern holds.

Now check second cross:
- Top = 9
- Bottom = 17
- Left = 5
- Right = 13

Then:
- Bottom - Top = 17 - 9 = 8
- Right - Left = 13 - 5 = 8 → same!

So the pattern holds for all three crosses.

But that doesn’t tell us what the center number is.

So far, we only know that:
> Bottom - Top = Right - Left

That’s consistent, but doesn't help us find the center value yet.

We need another clue.

Let’s now look at the center number and see if it relates to the others.

Try: Is the center number related to the average or sum?

Back to first cross:
- Numbers: 7, 4, 10, 13 → sum = 34
- Center = 3 → 34 / 3 ≈ 11.3 → no

Try: Maybe center = (Top + Left + Right + Bottom) / k?

Or perhaps: center = (Top + Bottom) - (Left + Right)

First cross:
- (7 + 13) = 20
- (4 + 10) = 14
- 20 - 14 = 6 → not 3

But 6 / 2 = 3 → interesting!

Try:
((Top + Bottom) - (Left + Right)) / 2 = ?

First cross:
- (7 + 13) = 20
- (4 + 10) = 14
- 20 - 14 = 6
- 6 / 2 = 3 → matches center!

Now test on third cross:
- Top = 9, Bottom = 23 → sum = 32
- Left = 2, Right = 16 → sum = 18
- 32 - 18 = 14
- 14 / 2 = 7 → matches center!

Perfect!

Now apply to second cross:
- Top = 9, Bottom = 17 → sum = 26
- Left = 5, Right = 13 → sum = 18
- Difference: 26 - 18 = 8
- Divide by 2: 8 / 2 = 4

So the missing number is 4.

Let’s verify:
- (Top + Bottom) = 9 + 17 = 26
- (Left + Right) = 5 + 13 = 18
- (26 - 18) / 2 = 8 / 2 = 4

Yes.

Also, check if the earlier pattern holds:
- Bottom - Top = 17 - 9 = 8
- Right - Left = 13 - 5 = 8 → same → consistent

So everything checks out.

✔ Final Answer: 4

The missing number is 4.