6th Grade Math Puzzles - Free Printable

Problem Description:

The task involves solving Sally's Hexagon Number Puzzle 4. Each hexagon is filled by adding the numbers in the two hexagons directly below it. The goal is to fill in the missing numbers in the puzzle.

Given Information:

- The puzzle consists of a series of hexagons arranged in a triangular pattern.
- Each hexagon (except those at the bottom row) contains a number that is the sum of the two hexagons directly below it.
- Some numbers are already provided, and we need to find the missing numbers.

Step-by-Step Solution:

#### Step 1: Understand the Pattern
Each hexagon's value is the sum of the two hexagons directly below it. For example:
- If a hexagon has values \( A \) and \( B \) directly below it, then the value of the hexagon above them is \( A + B \).

#### Step 2: Identify Known Values
From the image, the known values are:
- Bottom row: \( 7, 6, 11, 18, 25, 32 \)
- Second row from the bottom: \( 13, 17, 29, 43, 57 \)
- Third row from the bottom: \( 30, 46, 72, 100 \)
- Fourth row from the bottom: \( 76, 118, 172 \)
- Fifth row from the bottom: \( 194, 290 \)
- Top row: \( ? \)

#### Step 3: Fill in Missing Values
We will work our way up from the bottom row to the top row, using the given values and the rule that each hexagon is the sum of the two hexagons below it.

##### Row 1 (Bottom Row):
The values are already given:
\[ 7, 6, 11, 18, 25, 32 \]

##### Row 2:
- The first hexagon: \( 7 + 6 = 13 \)
- The second hexagon: \( 6 + 11 = 17 \)
- The third hexagon: \( 11 + 18 = 29 \)
- The fourth hexagon: \( 18 + 25 = 43 \)
- The fifth hexagon: \( 25 + 32 = 57 \)

These values match the given values in Row 2:
\[ 13, 17, 29, 43, 57 \]

##### Row 3:
- The first hexagon: \( 13 + 17 = 30 \)
- The second hexagon: \( 17 + 29 = 46 \)
- The third hexagon: \( 29 + 43 = 72 \)
- The fourth hexagon: \( 43 + 57 = 100 \)

These values match the given values in Row 3:
\[ 30, 46, 72, 100 \]

##### Row 4:
- The first hexagon: \( 30 + 46 = 76 \)
- The second hexagon: \( 46 + 72 = 118 \)
- The third hexagon: \( 72 + 100 = 172 \)

These values match the given values in Row 4:
\[ 76, 118, 172 \]

##### Row 5:
- The first hexagon: \( 76 + 118 = 194 \)
- The second hexagon: \( 118 + 172 = 290 \)

These values match the given values in Row 5:
\[ 194, 290 \]

##### Row 6 (Top Row):
- The top hexagon: \( 194 + 290 = 484 \)

#### Step 4: Verify the Solution
By following the rule that each hexagon is the sum of the two hexagons below it, all calculations are consistent with the given values.

Final Answer:

The missing number in the top hexagon is:
\[
\boxed{484}
\]