Let's solve the
Pyramid Puzzle step by step.
---
🔍 Understanding the Puzzle
We are given two pyramids made of circles. Each circle must be filled with a
whole number, such that:
>
The value of each circle is the sum of the two circles directly below it.
This is similar to Pascal’s triangle, but with specific numbers at the base (bottom row), and we need to fill in the upper rows accordingly.
We have
two separate pyramids:
---
## 🔹
First Pyramid:
```
?
? ?
? ? ?
3 1 2 1 0
```
Wait — actually, looking closely, the first pyramid has
5 circles in the bottom row:
`3`, `1`, `2`, `1`, `0`
So this pyramid has
5 levels:
- Level 1 (top): 1 circle
- Level 2: 2 circles
- Level 3: 3 circles
- Level 4: 4 circles
- Level 5 (bottom): 5 circles
But the diagram shows only
4 rows above the bottom one? Let's re-express it properly.
Looking at the image layout:
```
?
? ?
? ? ?
? ? ? ?
3 1 2 1 0
```
Wait — actually, the bottom row has
5 numbers: 3, 1, 2, 1, 0 → so there are
5 circles in the base, meaning the pyramid has
5 levels.
But the diagram only shows
4 rows above the base? No — let's count the rows:
- Row 1 (top): 1 circle
- Row 2: 2 circles
- Row 3: 3 circles
- Row 4: 4 circles
- Row 5 (bottom): 5 circles
Yes — so we go from bottom up.
We are given the
bottom row:
3, 1, 2, 1, 0
We need to compute the values
above using the rule:
> Each circle = sum of the
two circles directly below it
So we work
from bottom to top, computing each level.
---
✔ Step 1: Bottom Row (Level 5)
```
3 1 2 1 0
```
✔ Step 2: Level 4 (4 circles)
Each circle is the sum of two adjacent numbers below:
- First: 3 + 1 =
4
- Second: 1 + 2 =
3
- Third: 2 + 1 =
3
- Fourth: 1 + 0 =
1
→ Level 4:
4, 3, 3, 1
✔ Step 3: Level 3 (3 circles)
- 4 + 3 =
7
- 3 + 3 =
6
- 3 + 1 =
4
→ Level 3:
7, 6, 4
✔ Step 4: Level 2 (2 circles)
- 7 + 6 =
13
- 6 + 4 =
10
→ Level 2:
13, 10
✔ Step 5: Level 1 (Top circle)
- 13 + 10 =
23
→ Top circle:
23
---
🟩 So the completed first pyramid is:
```
23
13 10
7 6 4
4 3 3 1
3 1 2 1 0
```
✔ First pyramid solved!
---
## 🔹
Second Pyramid:
Now we do the same for the second pyramid.
Given bottom row:
2, 2, 1, 3
So this pyramid has
4 levels:
- Level 4 (bottom): 4 circles
- Level 3: 3 circles
- Level 2: 2 circles
- Level 1: 1 circle (top)
✔ Step 1: Bottom Row (Level 4)
```
2 2 1 3
```
✔ Step 2: Level 3
- 2 + 2 =
4
- 2 + 1 =
3
- 1 + 3 =
4
→ Level 3:
4, 3, 4
✔ Step 3: Level 2
- 4 + 3 =
7
- 3 + 4 =
7
→ Level 2:
7, 7
✔ Step 4: Level 1 (Top)
- 7 + 7 =
14
→ Top circle:
14
---
🟩 Completed second pyramid:
```
14
7 7
4 3 4
2 2 1 3
```
---
##
✔ Final Answer:
First Pyramid (Top number):
23
Second Pyramid (Top number):
14
---
📌 Summary:
- The rule is:
each circle = sum of the two circles immediately below it.
- We build
upward from the base.
- All values are whole numbers (as required).
---
✔ Answer:
- Top of first pyramid:
23
- Top of second pyramid:
14
Parent Tip: Review the logic above to help your child master the concept of critical thinking worksheet for elementary students.
