Let's analyze the pattern in the given diamond-shaped figures.
We have three diamonds, each with numbers at the four corners and one number in the center. The goal is to find the missing number in the third diamond.
Here are the figures:
---
First Diamond:
```
1
5 5
6
3
```
Second Diamond:
```
3
8 7
8
4
```
Third Diamond:
```
1
4 9
(?)
5
```
We need to find a relationship between the corner numbers and the center number.
Let’s denote:
- Top: T
- Right: R
- Bottom: B
- Left: L
- Center: C
We will look for a pattern using the first two diamonds.
---
First Diamond:
- T = 1
- R = 5
- B = 3
- L = 5
- C = 6
Try possible operations.
Let’s try:
Is it (T + B) × something?
(1 + 3) = 4 → not 6.
(L + R) = 5 + 5 = 10 → too big.
What if: (L + R) / (T + B)?
(5 + 5)/(1 + 3) = 10/4 = 2.5 → no.
Try: (L × R) / (T + B)?
(5×5)/(1+3) = 25/4 = 6.25 → close but not 6.
Try: (T + R + B + L) = 1 + 5 + 3 + 5 = 14 → not 6.
Wait — maybe it's
sum of opposite sides?
Opposite pairs:
- Top and Bottom: 1 + 3 = 4
- Left and Right: 5 + 5 = 10
No clear relation.
Alternatively, think:
is the center number related to the product or sum of adjacent numbers?
Try: (Left × Right) - (Top × Bottom)?
For first diamond:
(5 × 5) - (1 × 3) = 25 - 3 = 22 → not 6.
(Left + Right) × (Top + Bottom)?
(5+5) × (1+3) = 10 × 4 = 40 → too big.
Wait — what if the center is the
average of the four numbers?
(1 + 5 + 3 + 5)/4 = 14/4 = 3.5 → no.
Try: Is it
(Left + Right) / (Top + Bottom)?
(5+5)/(1+3) = 10/4 = 2.5 → no.
Hmm.
Try another idea: Maybe the
center number is the result of some operation involving all four corners.
Look at second diamond:
Second Diamond:
- T = 3
- R = 7
- B = 4
- L = 8
- C = 8
Now check:
Sum: 3 + 7 + 4 + 8 = 22 → not 8.
Product? Way too big.
Try: (L + R) = 8 + 7 = 15 → not 8.
(T + B) = 3 + 4 = 7 → close to 8.
(L + R) = 15 → too big.
Wait — try: (L × B) / (T × R) ?
(8 × 4)/(3 × 7) = 32/21 ≈ 1.5 → no.
Try: (L + R) - (T + B) = (8+7) - (3+4) = 15 - 7 = 8 → YES! That matches the center.
Check first diamond:
(L + R) - (T + B) = (5 + 5) - (1 + 3) = 10 - 4 = 6 → YES! Matches center.
So the rule seems to be:
>
Center = (Left + Right) - (Top + Bottom)
Let’s verify:
First Diamond:
(5 + 5) - (1 + 3) = 10 - 4 = 6
✔
Second Diamond:
(8 + 7) - (3 + 4) = 15 - 7 = 8
✔
Now apply to
Third Diamond:
- T = 1
- R = 9
- B = 5
- L = 4
- C = ?
C = (L + R) - (T + B) = (4 + 9) - (1 + 5) = 13 - 6 =
7
✔ So the missing number is
7.
---
Final Answer:
$$
\boxed{7}
$$
Explanation:
The center number is calculated as:
>
(Left + Right) - (Top + Bottom)
Applying this:
- Third diamond: (4 + 9) - (1 + 5) = 13 - 6 = 7
Thus, the missing number is
7.
Parent Tip: Review the logic above to help your child master the concept of printable iq tests with answers.