Math Puzzle Worksheets For Kids in 1st to 6th Grades | edHelper.com - Free Printable

Problem Analysis

The task involves filling in the missing blocks in a pyramid structure where each block above is the sum of the two blocks directly below it. The given information includes:
- The bottom row of the pyramid: `2`, `16.11`, `5.9`, `19.5`, `15.3`, `13`, `18.7`.
- One intermediate value in the second row from the bottom: `22.01`.
- The topmost value in the pyramid: `903.36`.

We need to determine the missing values in the pyramid by working upwards step by step.

---

Step-by-Step Solution

#### Step 1: Understand the Pyramid Structure
The pyramid is structured such that:
- Each block is the sum of the two blocks directly below it.
- We start from the bottom and work our way up to fill in the missing values.

#### Step 2: Fill in the Second Row from the Bottom
The second row from the bottom has one known value (`22.01`) and several unknowns. Let's denote the blocks in this row as follows:
```
? ? ? ? ?
/ \ / \ / \ / \ / \
2 16.11 5.9 19.5 15.3 13 18.7
```
We know:
- The second block in this row is `22.01`, which is the sum of `16.11` and `5.9`:
$$
16.11 + 5.9 = 22.01
$$

Now, let's calculate the other blocks in this row:
1. The first block is the sum of `2` and `16.11`:
$$
2 + 16.11 = 18.11
$$

2. The third block is the sum of `5.9` and `19.5`:
$$
5.9 + 19.5 = 25.4
$$

3. The fourth block is the sum of `19.5` and `15.3`:
$$
19.5 + 15.3 = 34.8
$$

4. The fifth block is the sum of `15.3` and `13`:
$$
15.3 + 13 = 28.3
$$

5. The sixth block is the sum of `13` and `18.7`:
$$
13 + 18.7 = 31.7
$$

So, the second row from the bottom is:
```
18.11 22.01 25.4 34.8 28.3 31.7
```

#### Step 3: Fill in the Third Row from the Bottom
Now, we move to the third row from the bottom. Let's denote the blocks in this row as follows:
```
? ? ? ?
/ \ / \ / \ / \
18.11 22.01 25.4 34.8 28.3 31.7
```
We calculate each block in this row:
1. The first block is the sum of `18.11` and `22.01`:
$$
18.11 + 22.01 = 40.12
$$

2. The second block is the sum of `22.01` and `25.4`:
$$
22.01 + 25.4 = 47.41
$$

3. The third block is the sum of `25.4` and `34.8`:
$$
25.4 + 34.8 = 60.2
$$

4. The fourth block is the sum of `34.8` and `28.3`:
$$
34.8 + 28.3 = 63.1
$$

5. The fifth block is the sum of `28.3` and `31.7`:
$$
28.3 + 31.7 = 60.0
$$

So, the third row from the bottom is:
```
40.12 47.41 60.2 63.1 60.0
```

#### Step 4: Fill in the Fourth Row from the Bottom
Next, we move to the fourth row from the bottom. Let's denote the blocks in this row as follows:
```
? ? ? ?
/ \ / \ / \ / \
40.12 47.41 60.2 63.1 60.0
```
We calculate each block in this row:
1. The first block is the sum of `40.12` and `47.41`:
$$
40.12 + 47.41 = 87.53
$$

2. The second block is the sum of `47.41` and `60.2`:
$$
47.41 + 60.2 = 107.61
$$

3. The third block is the sum of `60.2` and `63.1`:
$$
60.2 + 63.1 = 123.3
$$

4. The fourth block is the sum of `63.1` and `60.0`:
$$
63.1 + 60.0 = 123.1
$$

So, the fourth row from the bottom is:
```
87.53 107.61 123.3 123.1
```

#### Step 5: Fill in the Fifth Row from the Bottom (Top Row)
Finally, we move to the top row. Let's denote the blocks in this row as follows:
```
? ? ?
/ \ / \ / \
87.53 107.61 123.3 123.1
```
We calculate each block in this row:
1. The first block is the sum of `87.53` and `107.61`:
$$
87.53 + 107.61 = 195.14
$$

2. The second block is the sum of `107.61` and `123.3`:
$$
107.61 + 123.3 = 230.91
$$

3. The third block is the sum of `123.3` and `123.1`:
$$
123.3 + 123.1 = 246.4
$$

So, the fifth row from the bottom is:
```
195.14 230.91 246.4
```

#### Step 6: Verify the Top Block
The top block is the sum of `195.14` and `230.91`:
$$
195.14 + 230.91 = 426.05
$$
And the sum of `230.91` and `246.4`:
$$
230.91 + 246.4 = 477.31
$$
Finally, the top block is the sum of `426.05` and `477.31`:
$$
426.05 + 477.31 = 903.36
$$
This matches the given top value, confirming our calculations are correct.

---

Final Answer

The completed pyramid is:
```
903.36
/ \
426.05 477.31
/ \ / \
195.14 230.91 246.4
/ \ / \ / \
87.53 107.61 123.3 123.1
/ \/ \/ \/ \
40.12 47.41 60.2 63.1 60.0
/ \/ \/ \/ \/ \
18.11 22.01 25.4 34.8 28.3 31.7
/ \/ \/ \/ \/ \/ \
2 16.11 5.9 19.5 15.3 13 18.7
```

Thus, the missing blocks are:
$$
\boxed{18.11, 25.4, 34.8, 28.3, 31.7, 40.12, 47.41, 60.2, 63.1, 60.0, 87.53, 107.61, 123.3, 123.1, 195.14, 230.91, 246.4}
$$