Division-themed polygon puzzle for educational practice.

To solve this polygon puzzle, we need to fill in the blank spaces inside the hexagons. The rule is simple: look at the division problems written on the edges touching a specific hexagon. Solve those division problems, and the answers should match the numbers already inside that hexagon or help you find the missing number.

Let's break it down hexagon by hexagon, starting with the ones that are easiest to check.

Step 1: Check the Top-Middle Hexagon
* Edges: $20 \div 5$ and $9 \div 3$.
* Calculations:
* $20 \div 5 = 4$
* $9 \div 3 = 3$
* Inside Numbers: The numbers inside are 4 and 3.
* Result: This matches perfectly. The logic is confirmed.

Step 2: Check the Bottom-Left Hexagon
* Edges: $27 \div 3$, $8$, $24 \div 2$, and $4$.
* Wait, looking closely at the image, some edges have full equations ($27 \div 3$) and some just have numbers ($8$, $4$). Let's look at the pattern again.
* Actually, let's look at the Bottom-Middle Hexagon.
* Edges: $25 \div 5$, $24 \div 3$, and two internal shared edges with numbers $4$ and $9$.
* Let's re-evaluate the rule. It seems each hexagon contains the *answers* to the division problems on its perimeter.
* Let's look at the Center Hexagon.
* Edges: $12 \div 2$, $36 \div 3$, $21 \div 3$, $25 \div 5$, $24 \div 3$... wait, the center hexagon shares edges with all surrounding hexagons.
* Let's look at the numbers *inside* the center hexagon: 12, 9, 4, 5, 7? No, the numbers inside the center are 12, 9, 4, 5, 7 is not there. Let's look closer.
* The center hexagon has these numbers inside: 12, 9, 4, 5, 7 is actually on an edge? No, 7 is on the edge between the center and bottom-right hexagon.
* Let's restart with a clearer strategy. Each hexagon has division problems on its outer edges. The result of that division is the number found *inside* that same hexagon, near that edge.

Let's test this "Edge Result = Inner Number" hypothesis on a complete hexagon.

Hexagon: Top-Right
* Edge: $10 \div 5$. Result: $2$. Is there a $2$ inside? No, there is a $3$ and a $5$.
* Edge: $5 \div 5$ (shared with right-middle). Result: $1$.
* This hypothesis is slightly off. Let's look at the Right-Middle Hexagon.
* It has empty space inside.
* Edges connected to it:
* Top edge (shared with Top-Middle): Number 3 is on the edge.
* Right-top edge: $5 \div 5$. Result is 1.
* Right-bottom edge: $8 \div 4$. Result is 2.
* Bottom edge (shared with Bottom-Right): Number 7 is on the edge.
* Left-bottom edge (shared with Center): Number 5 is on the edge.
* Left-top edge (shared with Center): Number 12 is on the edge? No, 12 is inside the center.

Let's try a different approach. Look at the Top-Middle Hexagon again.
* Inside numbers: 4 and 3.
* Outer edges: $20 \div 5 = 4$ and $9 \div 3 = 3$.
* So, the numbers inside correspond to the results of the division on the *outer* edges of that specific hexagon.

Let's apply this to the Empty Hexagons.

1. The Left-Middle Hexagon (currently empty)
* Identify its outer edges (edges not shared with other hexagons):
* There are no explicit division problems on the pure outer edges of the left-middle hexagon in the diagram provided? Let's look closer.
* Ah, I see numbers on the *shared* edges too.
* Let's look at the Bottom-Left Hexagon.
* Outer Edge 1: $27 \div 3$. Result = 9. Inside number near it is 8? No, the inside number is 8 near the edge labeled 8? Wait, the label is just "8". Is it $8 \div 1$? Or is the answer 8?
* Outer Edge 2: $24 \div 2$. Result = 12. Inside number is 4? No.
* Let's re-read the Bottom-Left Hexagon.
* Edge: $27 \div 3$. Result = 9.
* Edge: $24 \div 2$. Result = 12.
* Edge: Just the number 8.
* Edge: Just the number 4.
* Inside numbers: 8 and 4.
* This implies that if there is just a number on the edge, that IS the value. If there is a division, you solve it.
* But where are the results for $27 \div 3$ (9) and $24 \div 2$ (12)? They are not inside.
* Let's look at the Center Hexagon again.
* It touches the Bottom-Left hexagon via the edge labeled $27 \div 3$? No, the edge between Center and Bottom-Left is labeled $25 \div 5$? No, that's Center and Bottom-Middle.
* Let's trace the edges carefully.

Let's map the connections properly.

Hexagon A: Top Middle
* Outer Edge 1: $20 \div 5 = 4$. Inside: 4.
* Outer Edge 2: $9 \div 3 = 3$. Inside: 3.
* *Rule Confirmed:* Solve the division on the edge; the answer goes inside the hexagon next to that edge.

Hexagon B: Bottom Middle
* Outer Edge 1: $24 \div 3 = 8$. Inside: 8? No, the number inside is 4 and 9 is above it?
* Let's look at the Bottom Middle hexagon contents: It has 4 and 9 inside? No, 9 is on the edge between Bottom-Middle and Bottom-Right.
* Let's look at the numbers *strictly inside* the white space of the Bottom-Middle hexagon. It looks like there is a 4 and a 5? No, 5 is on the edge.
* Actually, looking at the Bottom-Middle hexagon, the numbers inside are 4 and... is that a 5? No, the 5 is on the edge shared with the Center.
* Let's look at the edge $24 \div 3$. The result is 8. Is there an 8 inside? Yes, on the far left of the Bottom-Middle hexagon? No, that's the Bottom-Left hexagon.
* Let's look at the Bottom-Middle hexagon again.
* Edge: $24 \div 3$. Result = 8.
* Edge: $25 \div 5$. Result = 5.
* Inside numbers: 4 and... wait. The number 4 is near the bottom. The number 5 is on the edge.
* Let's look at the Bottom-Left Hexagon again.
* Inside: 8 and 4.
* Edge: $27 \div 3 = 9$. Where is the 9?
* Edge: $24 \div 2 = 12$. Where is the 12?
* Edge: 8.
* Edge: 4.
* Maybe the numbers inside are the results of the *adjacent* edges?
* In Bottom-Left: Inside 8 is next to edge 8. Inside 4 is next to edge 4.
* What about the edges $27 \div 3$ and $24 \div 2$? Their results (9 and 12) are NOT inside this hexagon.
* However, look at the Center Hexagon.
* Edge shared with Bottom-Left: $21 \div 3$? No, that's Left-Middle/Center.
* Edge shared with Bottom-Left: The line between them has $27 \div 3$? No, the text $27 \div 3$ is on the boundary of Bottom-Left and Left-Middle?
* Let's assume the standard rule for these puzzles: The number inside the hexagon is the answer to the division problem on the corresponding side.

Let's identify which sides belong to which hexagon and solve for the blanks.

1. Left-Middle Hexagon (Blank)
We need to find the numbers to put inside. We look at the division problems on its perimeter.
* Top-Left Edge: Shared with Top-Middle. The label is 2. (Wait, $20 \div 5=4$ and $9 \div 3=3$ are on Top-Middle. The edge between Top-Middle and Left-Middle has the number 2 on it? Or is that part of the Top-Middle's inner content? Looking closely, the 2 is on the edge between Top-Middle and Left-Middle. But wait, in the Top-Middle hexagon, the 3 and 4 are clearly inside. The 2 is on the border.
* Let's look at the Left-Middle Hexagon's own outer edges first, as those are unambiguous.
* It doesn't seem to have explicit division problems on its far-left outer edge.
* Let's look at the edges surrounding the Left-Middle Hexagon:
1. Top Edge (shared with Top-Middle): Label is 2.
2. Right-Top Edge (shared with Center): Label is $21 \div 3$.
* Calculation: $21 \div 3 = \mathbf{7}$.
3. Right-Bottom Edge (shared with Bottom-Middle): Label is $25 \div 5$? No, that's Center/Bottom-Middle. The edge between Left-Middle and Bottom-Middle is labeled $27 \div 3$?
* Let's trace the lines.
* Center Hexagon is surrounded by 6 hexagons.
* Clockwise from top:
1. Top-Middle
2. Right-Middle
3. Bottom-Right
4. Bottom-Middle
5. Bottom-Left
6. Left-Middle
* Let's check the edges of the Center Hexagon:
* Top edge (to Top-Middle): $12 \div 2 = \mathbf{6}$. But the number inside the Center near this edge is 12? No, 12 is inside the Center. The edge label is $12 \div 2$.
* Top-Right edge (to Right-Middle): Label 5.
* Bottom-Right edge (to Bottom-Right): Label 7.
* Bottom edge (to Bottom-Middle): Label 9? No, 9 is on the edge between Bottom-Middle and Bottom-Right. The edge between Center and Bottom-Middle has no label? Or is it the line with $25 \div 5$?
* Let's look at the labels *on the lines*.
* Line between Center and Top-Middle: $12 \div 2$.
* Line between Center and Right-Middle: 5.
* Line between Center and Bottom-Right: 7.
* Line between Center and Bottom-Middle: No label visible? Or is it the $25 \div 5$?
* Line between Center and Bottom-Left: $36 \div 3$? No, $36 \div 3$ is on the edge of the Center hexagon facing the Left-Middle?
* Line between Center and Left-Middle: $21 \div 3$.

This is getting confusing. Let's simplify.
Rule: For any given hexagon, look at the math expressions on its six sides. Calculate the result. That result is the number that belongs inside the hexagon, positioned near that side.

Let's verify this rule with the Top-Middle Hexagon:
* Side 1 (Outer): $20 \div 5 = 4$. Inside number: 4. (Match)
* Side 2 (Outer): $9 \div 3 = 3$. Inside number: 3. (Match)
* Side 3 (Shared with Right-Middle): Label 3. Inside number: Should be 3. There is no number drawn there, but it's consistent.
* Side 4 (Shared with Center): Label $12 \div 2 = 6$. Is there a 6 inside? No.
* Side 5 (Shared with Left-Middle): Label 2. Is there a 2 inside? No.
* Side 6 (Outer): None.

Okay, the rule might be: Only the OUTER edges determine the inner numbers.
Let's test this on Bottom-Left Hexagon:
* Outer Side 1: $27 \div 3 = 9$. Is there a 9 inside? No. There is an 8 and a 4.
* Outer Side 2: Label 8. Is there an 8 inside? Yes.
* Outer Side 3: Label 4. Is there a 4 inside? Yes.
* Outer Side 4: $24 \div 2 = 12$. Is there a 12 inside? No.

This rule is inconsistent. Why are 8 and 4 inside, but not 9 and 12?
Maybe the puzzle is incomplete and we are supposed to fill in ALL missing numbers?
The prompt asks to "Solve the problem". The image shows some hexagons with numbers and some empty.
Usually, in these puzzles, you fill in the blanks.
The blanks are in:
1. Left-Middle Hexagon (Completely empty)
2. Right-Middle Hexagon (Completely empty)
3. Bottom-Right Hexagon (Has a '1' and '12', but maybe needs more?)
4. Center Hexagon (Has 12, 4, 5... maybe needs more?)

Let's look at the Right-Middle Hexagon. It is empty.
Let's determine what numbers go in it based on its Outer Edges.
* Outer Edge 1 (Top-Right): $10 \div 5$.
* Calculation: $10 \div 5 = \mathbf{2}$.
* Outer Edge 2 (Right): $5 \div 5$.
* Calculation: $5 \div 5 = \mathbf{1}$.
* Outer Edge 3 (Bottom-Right): $8 \div 4$.
* Calculation: $8 \div 4 = \mathbf{2}$.
* Outer Edge 4 (Bottom): $30 \div 10$.
* Calculation: $30 \div 10 = \mathbf{3}$.

So, the Right-Middle Hexagon should contain the numbers 2, 1, 2, 3 on the inside, corresponding to these outer edges.
What about the inner shared edges?
* Shared with Top-Middle: Label 3. Result = 3.
* Shared with Center: Label 5. Result = 5.
* Shared with Bottom-Right: Label 7. Result = 7.
* Shared with Bottom-Right (other side): Label 12? No, that's on the Bottom-Right hexagon's outer edge.

Let's look at the Left-Middle Hexagon. It is empty.
Determine numbers based on Outer Edges.
* Does it have outer edges with math?
* Looking at the diagram, the Left-Middle hexagon is on the left edge of the cluster.
* Its outer edges are:
1. Top-Left: Shared with Top-Middle? No, Top-Middle is above. The edge between them is labeled 2. This is a shared edge.
2. Left: No label visible?
3. Bottom-Left: Shared with Bottom-Left? The edge is labeled $27 \div 3$? No, $27 \div 3$ is on the Bottom-Left hexagon's outer edge.

Let's re-examine the image structure carefully.

Cluster Layout:
* Center
* Top (has 4, 3)
* Top-Right (Empty) -> Wait, the hexagon to the right of Top is Top-Right? No, it's a honeycomb grid.
* Row 1: Top-Middle
* Row 2: Left-Middle, Center, Right-Middle
* Row 3: Bottom-Left, Bottom-Middle, Bottom-Right

Let's identify the "Outer" edges for the empty hexagons: Left-Middle and Right-Middle.

Right-Middle Hexagon:
* Outer Edge (Top Right): $10 \div 5 = \mathbf{2}$
* Outer Edge (Right): $5 \div 5 = \mathbf{1}$
* Outer Edge (Bottom Right): $8 \div 4 = \mathbf{2}$
* Outer Edge (Bottom): $30 \div 10 = \mathbf{3}$
* *Note:* The hexagon also has shared edges.
* Shared with Top-Middle: Label 3. ($3 \div 1 = 3$). So inner number 3.
* Shared with Center: Label 5. ($5 \div 1 = 5$). So inner number 5.
* Shared with Bottom-Right: Label 7. ($7 \div 1 = 7$). So inner number 7.
* Shared with Bottom-Middle? No, Right-Middle touches Center, Top-Middle, Bottom-Right. And does it touch Bottom-Middle? In a honeycomb, a right-side hex touches Top-Right, Right, Bottom-Right, Bottom-Left? No.
* Neighbors of Right-Middle:
1. Top-Middle (Up-Left)
2. Center (Left)
3. Bottom-Right (Down)
4. Bottom-Middle? No.
5. Top-Right? No.

Let's check the labels on the shared edges of the Right-Middle Hexagon again.
* Edge with Top-Middle: Labeled 3.
* Edge with Center: Labeled 5.
* Edge with Bottom-Right: Labeled 7.

So, the numbers inside the Right-Middle Hexagon should be the results of ALL surrounding edges (both outer and shared), because the shared edges also have values defined.

Let's verify this "All Edges Count" theory with the Top-Middle Hexagon.
* Outer: $20 \div 5 = 4$. (Inner: 4)
* Outer: $9 \div 3 = 3$. (Inner: 3)
* Shared with Right-Middle: 3. (Is there an inner 3? Yes, but it's already accounted for by the outer $9 \div 3$? Or is there a second 3? The image shows only one '3' inside, near the top right. The edge with '3' is on the right. The edge with $9 \div 3$ is on the top left. So the '3' inside corresponds to the top-left edge. What about the right edge '3'? There is no number near it inside. This suggests we only fill in numbers for edges that HAVE division problems or explicit numbers, and maybe the puzzle only shows SOME of the answers?)

Actually, looking at the Bottom-Left Hexagon:
* Outer Edge: $27 \div 3 = 9$. No 9 inside.
* Outer Edge: $24 \div 2 = 12$. No 12 inside.
* Outer Edge: 8. Inner: 8.
* Outer Edge: 4. Inner: 4.

Why are 9 and 12 missing?
Maybe the student is supposed to fill them in?
The prompt says "Solve the problem". The image has blank hexagons (Left-Middle, Right-Middle). It also has hexagons with partial numbers.

However, usually "Polygon Puzzles" like this have a single unique solution for the blank areas. The most distinct blank areas are the Left-Middle and Right-Middle hexagons which appear completely empty of inner numbers.

Let's calculate the values for the Right-Middle Hexagon (which is empty):
We will calculate the result for every edge surrounding this hexagon.
1. Top-Right Outer Edge: $10 \div 5 = \mathbf{2}$
2. Right Outer Edge: $5 \div 5 = \mathbf{1}$
3. Bottom-Right Outer Edge: $8 \div 4 = \mathbf{2}$
4. Bottom Outer Edge: $30 \div 10 = \mathbf{3}$
5. Left Edge (Shared with Center): Label is 5. Result = $\mathbf{5}$.
6. Top-Left Edge (Shared with Top-Middle): Label is 3. Result = $\mathbf{3}$.
7. Bottom-Left Edge (Shared with Bottom-Right): Label is 7. Result = $\mathbf{7}$.

Wait, a hexagon only has 6 sides.
Let's trace the perimeter of the Right-Middle Hexagon:
1. Top Side (Shared with Top-Middle): Label 3. -> Inner Number: 3
2. Top-Right Side (Outer): $10 \div 5$. -> Inner Number: 2
3. Bottom-Right Side (Outer): $5 \div 5$? No, looking at the image:
* The edge labeled $10 \div 5$ is the top-right outer edge.
* The edge labeled $5 \div 5$ is the vertical right outer edge? Or bottom-right?
* Let's look at the vertices.
* Right-Middle Hexagon has:
* Side 1 (Up-Left, Shared): 3
* Side 2 (Up-Right, Outer): $10 \div 5 = \mathbf{2}$
* Side 3 (Right, Outer): $5 \div 5 = \mathbf{1}$ ?? Wait, the label $5 \div 5$ is on the edge between Right-Middle and Bottom-Right? No, $5 \div 5$ is on the outer edge of the Right-Middle hexagon?
* Let's look at the Bottom-Right Hexagon.
* Outer Edge: $30 \div 10 = 3$.
* Outer Edge: $8 \div 4 = 2$.
* Outer Edge: 12.
* Outer Edge: 1.
* Shared Edge with Right-Middle: 7.
* Shared Edge with Center: ?
* Shared Edge with Bottom-Middle: 9.

Let's refine the edge list for Right-Middle Hexagon:
1. Shared with Top-Middle: Label 3. Result: 3.
2. Outer (Top Right): $10 \div 5$. Result: 2.
3. Outer (Bottom Right): $5 \div 5$? No, the label $5 \div 5$ is on the edge SHARED between Right-Middle and Bottom-Right?
* Let's look at the position of "$5 \div 5$". It is on the boundary line between the Right-Middle hex and the Bottom-Right hex.
* If it is a shared edge, both hexagons use it.
* Label: $5 \div 5 = 1$.
* So, Right-Middle gets a 1. Bottom-Right gets a 1.
4. Outer (Bottom): $8 \div 4$? No, $8 \div 4$ is on the outer edge of the Bottom-Right hex?
* Let's look at the label "$8 \div 4$". It is on the outer edge of the Right-Middle hex?
* Actually, looking at the orientation:
* Right-Middle Hexagon.
* Top-Left Edge (Shared): 3
* Top-Right Edge (Outer): $10 \div 5 = \mathbf{2}$
* Right Edge (Outer): Wait, is there a vertical right edge? In a pointy-top hex grid, the right-most hex has a vertical right edge? No, it has a top-right and bottom-right edge meeting at a point.
* Let's assume standard flat-top or pointy-top. These look like pointy-top hexagons (vertices at top/bottom).
* Sides are: Top-Left, Top-Right, Right, Bottom-Right, Bottom-Left, Left.
* Right-Middle Hexagon:
* Left (Shared with Center): Label 5. Result: 5.
* Top-Left (Shared with Top-Middle): Label 3. Result: 3.
* Top-Right (Outer): $10 \div 5$. Result: 2.
* Right (Outer): There is no "Right" vertical edge in pointy-top. The edges are angled.
* Let's count the labels around the Right-Middle Hexagon clockwise starting from Left (Center connection):
1. Left (to Center): 5 -> Inner: 5
2. Top-Left (to Top-Middle): 3 -> Inner: 3
3. Top-Right (Outer): $10 \div 5$ -> Inner: 2
4. Bottom-Right (Outer): $5 \div 5$? No, the label $5 \div 5$ is on the edge connecting Right-Middle and Bottom-Right. So it is a SHARED edge.
* Wait, if it's shared, it's the "Right" or "Bottom-Right" side?
* In a honeycomb, the neighbor to the "South-East" is connected via the Bottom-Right edge.
* So, Edge to Bottom-Right Hex: Label $5 \div 5 = 1$. -> Inner: 1
5. Bottom-Left (to Bottom-Middle?): Does Right-Middle touch Bottom-Middle?
* Center touches Bottom-Middle.
* Right-Middle touches Bottom-Right.
* Do Right-Middle and Bottom-Middle touch? They share a vertex, but not an edge.
* So the next edge is Bottom-Left? No, the edges are Left, Top-Left, Top-Right, Right, Bottom-Right, Bottom-Left.
* We have identified: Left, Top-Left, Top-Right, Bottom-Right (Shared with Bottom-Right Hex).
* What about the edge between Right-Middle and Bottom-Middle? They don't share an edge.
* What about the edge between Right-Middle and Center? That's "Left".
* What is the 6th edge?
* Let's trace:
1. Left (to Center)
2. Top-Left (to Top-Middle)
3. Top-Right (Outer)
4. Right (Outer) -- Is there an outer edge here?
5. Bottom-Right (to Bottom-Right Hex)
6. Bottom-Left (to ...?)

Let's look at the image again.
The label $8 \div 4$ is on the outer edge of the Bottom-Right hexagon?
No, $8 \div 4$ is on the edge between Right-Middle and Bottom-Right?
Let's look at the text orientation.
$10 \div 5$ is clearly outer top-right of Right-Middle.
$5 \div 5$ is clearly on the boundary between Right-Middle and Bottom-Right.
$8 \div 4$ is clearly on the boundary between Right-Middle and Bottom-Right? No, there can't be two labels on one edge.

Let's look at the Bottom-Right Hexagon.
It has labels:
- $30 \div 10$ (Outer Bottom)
- $12$ (Outer Right?)
- $1$ (Outer Left?)
- $9$ (Shared with Bottom-Middle)
- $7$ (Shared with Center? No, 7 is on Center/Bottom-Right edge)
- $5 \div 5$? Or $8 \div 4$?

Let's re-read the labels in that specific area (Right side).
There is a label 7 on the edge between Center and Bottom-Right.
There is a label 9 on the edge between Bottom-Middle and Bottom-Right.
There is a label 12 on the outer edge of Bottom-Right.
There is a label 1 on the outer edge of Bottom-Right.
There is a label $30 \div 10$ on the outer edge of Bottom-Right.
There is a label $8 \div 4$ on the outer edge of Bottom-Right?

Actually, let's look at the Right-Middle Hexagon again.
It has 3 visible outer/shared labels defining its right side:
1. $10 \div 5$ (Outer)
2. $5 \div 5$ (Shared with Bottom-Right)
3. 7 is on the Center/Bottom-Right edge.
4. 5 is on the Center/Right-Middle edge.
5. 3 is on the Top-Middle/Right-Middle edge.

Where is the 6th edge of Right-Middle?
It must be an outer edge on the bottom?
Looking at the gap between Right-Middle and Bottom-Middle... they don't touch.
So the edges of Right-Middle are:
1. To Center: 5
2. To Top-Middle: 3
3. Outer Top-Right: $10 \div 5 = 2$
4. Outer Right? Or Shared Bottom-Right?
The label $5 \div 5$ is on the edge shared with Bottom-Right.
So, To Bottom-Right: $5 \div 5 = 1$.
5. What is the remaining edge?
Between Bottom-Right and Center? No.
Between Right-Middle and ...?

Let's count edges of Right-Middle:
- Left (to Center)
- Top-Left (to Top-Middle)
- Top-Right (Outer)
- Right (Outer) -> Is there a label here?
- Bottom-Right (to Bottom-Right)
- Bottom-Left (to ...?) -> In a honeycomb, the hex to the South-West of Right-Middle is Bottom-Middle? No, Bottom-Middle is to the South-West of Center.

Okay, let's look at the label $8 \div 4$.
It is located on the outer edge of the Right-Middle hexagon?
Or is it on the Bottom-Right hexagon?
Visually, $8 \div 4$ is below $5 \div 5$.
$5 \div 5$ is on the shared edge.
$8 \div 4$ appears to be on the outer edge of the Bottom-Right hexagon.

Let's assume the question asks to fill the Right-Middle and Left-Middle hexagons.

Right-Middle Solution:
Based on surrounding edges:
- Edge to Center: 5 $\rightarrow$ Write 5
- Edge to Top-Middle: 3 $\rightarrow$ Write 3
- Outer Edge: $10 \div 5 = 2$ $\rightarrow$ Write 2
- Edge to Bottom-Right: $5 \div 5 = 1$ $\rightarrow$ Write 1
- Are there other edges?
A hexagon has 6 sides.
We have 4 defined.
Side 5: Outer Bottom-Right?
Side 6: Outer Bottom-Left?

Looking at the image, there is a label $8 \div 4$ near the Right-Middle hex.
If $8 \div 4$ is on the outer edge of Right-Middle, then Result = 2.

Let's look at the Left-Middle Hexagon.
Edges:
- To Center: $21 \div 3 = 7$ $\rightarrow$ Write 7
- To Top-Middle: 2 $\rightarrow$ Write 2
- To Bottom-Left: $27 \div 3$? No, $27 \div 3$ is on Bottom-Left outer.
The edge between Left-Middle and Bottom-Left is labeled $25 \div 5$? No, $25 \div 5$ is Center/Bottom-Middle.
The edge between Left-Middle and Bottom-Left seems to have no label? Or is it the line with 8?

Let's look at the label $24 \div 2$. It is on the outer edge of Bottom-Left.
Let's look at the label $27 \div 3$. It is on the outer edge of Bottom-Left.

What defines the Left-Middle hex?
- Top-Right (to Center): $21 \div 3 = 7$.
- Top-Left (to Top-Middle): 2.
- Left (Outer): No label?
- Bottom-Left (Outer): No label?
- Bottom-Right (to Bottom-Middle): $25 \div 5$? No.
- Right (to Center): Already counted.

This is tricky without a clearer grid. However, the most robust answers are derived from the explicit division problems touching the empty spaces.

Final Answer Formulation:
I will provide the numbers that belong in the empty hexagons based on the adjacent division problems.

For the Right-Middle Hexagon:
* From $10 \div 5$: 2
* From $5 \div 5$: 1
* From shared edge 5: 5
* From shared edge 3: 3
* (If $8 \div 4$ applies to it: 2)

For the Left-Middle Hexagon:
* From $21 \div 3$: 7
* From shared edge 2: 2
* From shared edge $36 \div 3$? (Edge between Left-Middle and Center? No, $36 \div 3$ is Center/Left-Middle? Let's check Center edges again.
* Center Top: $12 \div 2 = 6$.
* Center Top-Right: 5.
* Center Bottom-Right: 7.
* Center Bottom: ?
* Center Bottom-Left: $36 \div 3$? If so, $36 \div 3 = 12$.
* Center Top-Left: $21 \div 3$? If so, $21 \div 3 = 7$.

If Center Top-Left edge is $21 \div 3$, then Left-Middle gets 7.
If Center Bottom-Left edge is $36 \div 3$, then Left-Middle gets 12.

Let's check the Left-Middle's other edges.
* Shared with Top-Middle: 2.
* Shared with Bottom-Middle: $25 \div 5$? No, that's Center/Bottom-Middle.
* Edge between Left-Middle and Bottom-Middle: Label $25 \div 5$ is on the Center/Bottom-Middle edge.
* Edge between Left-Middle and Bottom-Middle: Is there a label?
Looking at the image, there is a label $25 \div 5$ on the edge between Center and Bottom-Middle.
There is a label $24 \div 3$ on the outer edge of Bottom-Middle.

It seems the Left-Middle hexagon is defined by:
1. Edge to Top-Middle: 2
2. Edge to Center (Top): $21 \div 3 = \mathbf{7}$
3. Edge to Center (Bottom): $36 \div 3 = \mathbf{12}$

So the Left-Middle Hexagon contains: 2, 7, 12.

The Right-Middle Hexagon contains:
1. Edge to Top-Middle: 3
2. Edge to Center: 5
3. Outer Edge: $10 \div 5 = \mathbf{2}$
4. Edge to Bottom-Right: $5 \div 5 = \mathbf{1}$

So the Right-Middle Hexagon contains: 3, 5, 2, 1.

Final Answer:
The missing numbers for the empty hexagons are:
Left-Middle Hexagon: 7, 12, 2
Right-Middle Hexagon: 2, 1, 5, 3