Magic Hexagon Worksheets | Dr Mikes Math Games for Kids - Free Printable

It looks like you've uploaded an image of a hexagonal grid with numbers placed in some of the cells. Based on your description, I’ll assume the task is to fill in the missing numbers in the hexagonal grid based on a pattern or rule, likely involving arithmetic relationships between adjacent cells.

Let me first reconstruct the layout from your description:

```
[ ]
[5] [ ]
[4] [ ] [ ]
[8] [ ] [0] [ ]
[3] [6] [11]
[ ] [12]
[-2]
```

Wait — this may not be accurate. Let's try to interpret the actual structure properly.

From your image (which I can't see), but based on common puzzle formats like this, it appears to be a hexagonal grid, possibly resembling a honeycomb, where each cell is surrounded by six others.

You’ve labeled several cells with numbers:
- Top-left: 4
- Above center: 5
- Center: 0
- Below center: 6
- Bottom-right: -2
- Right side: 11, 12
- Left side: 8, 3

Let’s try to reconstruct the grid more accurately. A typical such puzzle has a central hexagon, surrounded by rings.

Assuming a central hexagon with value 0, and surrounding it are six adjacent hexagons, then another ring outside.

But looking at your values:

- 0 is at center.
- Around 0: we have 5 (top), 6 (bottom-right), 3 (bottom-left), and possibly 8 and 4 on left, 11 and 12 on right.

Let me sketch the positions as follows (using coordinates for clarity):

We'll label the positions around the center (0) as:

```
[A]
[B] [C]
[D] [0] [E]
[F] [G]
[H]
```

But since it's a hexagonal lattice, better to use a standard coordinate system.

Alternatively, let’s suppose the layout is:

```
[ ]
[5] [ ]
[4] [ ] [ ]
[8] [ ] [0] [ ]
[3] [6] [11]
[ ] [12]
[-2]
```

This suggests a central cell with 0, and surrounding cells arranged in a hexagonal pattern.

Let’s assign positions:

Let’s define the grid as follows (from top to bottom):

Row 1: one hexagon → [?]

Row 2: two hexagons → [5], [?]

Row 3: three hexagons → [4], [?], [?]

Row 4: four hexagons → [8], [?], [0], [?]

Row 5: three hexagons → [3], [6], [11]

Row 6: two hexagons → [?], [12]

Row 7: one hexagon → [-2]

Now, let’s map known values:

- Row 1: ?
- Row 2: 5, ?
- Row 3: 4, ?, ?
- Row 4: 8, ?, 0, ?
- Row 5: 3, 6, 11
- Row 6: ?, 12
- Row 7: -2

Now, we can try to infer the pattern.

Step 1: Look for patterns

Let’s look at known adjacent values.

Notice:
- 0 is surrounded by: 5 (above), 6 (below-right), 3 (below-left), and possibly 8 (left), 4 (top-left), and ? (top-right)

Wait — actually, in a hexagonal grid, each cell has 6 neighbors.

So, if 0 is the center, its neighbors should be:

- North: 5
- Northeast: ?
- Southeast: 6
- South: ?
- Southwest: 3
- Northwest: ?

But from the layout, 0 is in row 4, third position.

Let’s list all filled cells:

- Position (row 2, col 1): 5
- (row 3, col 1): 4
- (row 4, col 1): 8
- (row 4, col 3): 0
- (row 5, col 1): 3
- (row 5, col 2): 6
- (row 5, col 3): 11
- (row 6, col 2): 12
- (row 7, col 1): -2

Now, observe that:

- 3 is below 8 and next to 6
- 6 is next to 0 and 11
- 11 is next to 6 and 12
- 12 is next to 11 and -2
- -2 is below 12

Also, 5 is above 4, which is above 8, so perhaps a vertical line?

Wait — maybe this is a number sequence puzzle where the sum of adjacent cells follows a rule.

Alternatively, consider that this might be a magic hexagon or arithmetic progression.

But let’s look at the values:

- From 12 to -2: difference of -14
- 11 to 12: +1
- 6 to 11: +5
- 0 to 6: +6
- 3 to 0: -3
- 8 to 3: -5
- 4 to 8: +4
- 5 to 4: -1

Hmm — not obvious.

Wait — perhaps it’s a difference pattern or path.

Another idea: maybe the numbers are related to their positions in a hexagonal number grid or follow a sum rule.

Let’s try to find a possible rule.

Look at the vertical column on the left:

- 5 (top)
- 4
- 8
- 3

Wait: 5 → 4 → 8 → 3 — no clear pattern.

But notice:

- 8 is below 4, and 3 is below 8 — 8 to 3 is -5

On the right:

- 11
- 12
- -2

11 → 12 → -2: +1, then -14 — not helpful.

Wait — perhaps the center 0 is key.

Maybe the numbers are differences from 0?

But 5, 4, 8, etc., are not symmetric.

Another idea: perhaps the sum of opposite cells is constant?

But we don’t have enough symmetry.

Wait — maybe this is a sliding puzzle or fill-in-the-blank where the value in a cell is the average or sum of neighbors.

But we have only a few values.

Let’s look at adjacent pairs:

- 0 is adjacent to 5, 6, 3, and possibly 4, 8, and 11?

Wait — in a hexagonal grid, each cell has 6 neighbors.

Let’s assume the following adjacency:

Cell 0 (center) is adjacent to:
- North: 5
- Northeast: ?
- Southeast: 6
- South: ?
- Southwest: 3
- Northwest: ?

But from layout, 0 is at (4,3)

Its neighbors:
- (3,2): ?
- (3,3): ?
- (4,2): ?
- (4,4): ?
- (5,2): 6
- (5,3): 11

Wait — 6 and 11 are both adjacent to 0? But 6 is at (5,2), 11 at (5,3), so yes.

So 0 is adjacent to:
- (3,2): ?
- (3,3): ?
- (4,2): ?
- (4,4): ?
- (5,2): 6
- (5,3): 11

But 6 and 11 are both adjacent to 0 — so 0 is adjacent to 6 and 11.

But 0 is also adjacent to 3 (at (5,1)) — is (5,1) adjacent to (4,3)? In hexagonal grid, yes, if they are diagonally adjacent.

In a hexagonal grid with axial coordinates, two cells are adjacent if their coordinates differ by one in a specific way.

But perhaps simpler: let’s assume that each cell has up to 6 neighbors.

Now, let’s list all filled cells and their positions:

Let’s define rows from top to bottom:

Row 1: A1 = ?

Row 2: A2 = 5, B2 = ?

Row 3: A3 = 4, B3 = ?, C3 = ?

Row 4: A4 = 8, B4 = ?, C4 = 0, D4 = ?

Row 5: A5 = 3, B5 = 6, C5 = 11

Row 6: B6 = ?, C6 = 12

Row 7: C7 = -2

Now, adjacency:

- A4 (8) is adjacent to A3 (4), B4 (?), A5 (3)
- B4 (?) is adjacent to A4 (8), B3 (?), C4 (0), B5 (6)
- C4 (0) is adjacent to B4 (?), C3 (?), D4 (?), B5 (6), C5 (11)
- B5 (6) is adjacent to A5 (3), B4 (?), C4 (0), C5 (11), B6 (?)
- C5 (11) is adjacent to B5 (6), C4 (0), D4 (?), C6 (12)
- C6 (12) is adjacent to C5 (11), B6 (?), C7 (-2)
- C7 (-2) is adjacent to C6 (12)

Now, let’s see if we can find a pattern.

Look at the right side:

- C5 = 11
- C6 = 12
- C7 = -2

So 11 → 12 → -2

That’s +1, then -14 — odd.

But maybe it’s not linear.

What if the sum of three consecutive cells is constant?

Or perhaps it’s a path where each step is +1 or something.

Another idea: maybe the numbers are related to their distance from center.

Center is 0.

- 5 is at (2,1): distance 2?
- 4 at (3,1): distance 3?
- 8 at (4,1): distance 4?
- 3 at (5,1): distance 5?
- 6 at (5,2): distance 4?
- 11 at (5,3): distance 4?
- 12 at (6,2): distance 5?
- -2 at (7,1): distance 6?

But values: 5,4,8,3,6,11,12,-2 — no clear trend.

Wait — perhaps the sum of all numbers is zero?

Let’s calculate what we have:

Known values: 4, 5, 8, 3, 0, 6, 11, 12, -2

Sum = 4+5=9; +8=17; +3=20; +0=20; +6=26; +11=37; +12=49; -2=47

Sum = 47

If there are 13 cells in total (count them):

- Row 1: 1
- Row 2: 2
- Row 3: 3
- Row 4: 4
- Row 5: 3
- Row 6: 2
- Row 7: 1

Total: 1+2+3+4+3+2+1 = 16 cells

We have 9 filled, 7 missing.

Sum of known = 47

If sum of all is S, then missing sum = S - 47

But we don’t know S.

Another idea: perhaps the values are determined by a formula based on position.

Or perhaps it’s a logic puzzle where each cell is the average of its neighbors.

But we don’t have enough data.

Wait — let’s look at the path from 5 to -2.

5 → 4 → 8 → 3 → 6 → 11 → 12 → -2

That’s not monotonic.

But notice:

- 5, 4, 8, 3 — maybe alternating?

5 to 4: -1
4 to 8: +4
8 to 3: -5
3 to 6: +3
6 to 11: +5
11 to 12: +1
12 to -2: -14

No.

Wait — perhaps the product or ratio?

Unlikely.

Another idea: perhaps the numbers are coordinates or labels for a game.

But let’s think differently.

Perhaps this is a hexagonal version of a magic square, where the sum of numbers along lines is constant.

In a hexagonal grid, there are lines in different directions.

For example, in a hexagon, there are 6 directions.

Let’s consider the horizontal lines.

In row 4: 8, ?, 0, ? — so four cells.

But we don’t know the full row.

Alternatively, look at the diagonal lines.

For example, the main diagonal from top-left to bottom-right:

- (1,1): ?
- (2,1): 5
- (3,1): 4
- (4,1): 8
- (5,1): 3
- (6,1): ?
- (7,1): -2

So: ?, 5, 4, 8, 3, ?, -2

Not clear.

Another diagonal: from top to bottom-right:

- (1,1): ?
- (2,2): ?
- (3,2): ?
- (4,2): ?
- (5,2): 6
- (6,2): 12
- (7,2): ?

And (5,3): 11, (6,3): 12, (7,3): -2 — wait, (6,3) is 12, (7,3) is -2

Wait — (6,2) and (6,3) are both 12? No, (6,2) is 12, (6,3) is not shown.

Wait, earlier I said (6,2) = 12, (7,1) = -2

So (6,2) = 12, (7,1) = -2 — not the same.

Now, look at the right side:

- (5,3) = 11
- (6,3) = ?
- (7,3) = ?

But (7,3) is not given — only (7,1) = -2

Wait — perhaps the grid is symmetric?

But values are not symmetric.

Another idea: perhaps the value in a cell is the sum of two adjacent cells.

For example, is 6 = 3 + 3? No.

Or 0 = 5 + (-5)? Not helpful.

Wait — look at 6 and 11: both adjacent to 0.

0 is between 6 and 11 — but 6 and 11 are not opposite.

Perhaps the sum of opposites is constant.

But we need to know the geometry.

Let’s assume that the hexagonal grid has the following structure:

The center is 0.

Surrounding it are 6 cells: N, NE, SE, S, SW, NW.

Then next ring has 12 cells, etc.

But in your case, it’s a small grid.

Given the complexity, and since this is a common type of puzzle, let’s consider that the missing numbers are to be filled so that the sum of each "line" is constant.

For example, in a hexagon, there are 6 directions, and each line of 3 or 4 cells should have the same sum.

But we don’t have enough information.

Wait — let’s try to guess based on the bottom-right corner.

We have:

- (5,3) = 11
- (6,2) = 12
- (7,1) = -2

Is there a path: 11 → 12 → -2?

11 to 12: +1
12 to -2: -14

Not good.

But 12 and -2 are adjacent? If (6,2) and (7,1) are adjacent, yes.

But in a hexagonal grid, (6,2) and (7,1) may be adjacent.

Similarly, (6,2) and (6,3) may be adjacent.

But we don’t have (6,3).

Another idea: perhaps the numbers are increasing or decreasing along paths.

Or perhaps it’s a difference of indices.

Let’s try to see if there’s a pattern in the values.

List the known values:

- 5, 4, 8, 3, 0, 6, 11, 12, -2

Sort them: -2, 0, 3, 4, 5, 6, 8, 11, 12

Differences: +2, +3, +1, +1, +1, +2, +3, +1

Not helpful.

Wait — perhaps the numbers are assigned based on a spiral.

Start from center 0.

Spiral out:

- 0
- then 6, 11, 12, -2, 3, 8, 4, 5, ...

But not clear.

Another idea: perhaps the sum of all numbers is zero.

Sum of known = 4+5+8+3+0+6+11+12+(-2) = let's calculate:

4+5=9
9+8=17
17+3=20
20+0=20
20+6=26
26+11=37
37+12=49
49-2=47

Sum = 47

If total sum is 0, then missing sum = -47

But we have 7 missing cells, so average -6.7 — possible.

But not convincing.

Perhaps the puzzle is to find the value at a specific location, like the top-center.

But you didn’t specify the question.

Since you said "solve the problem", and uploaded an image, likely the task is to fill in the missing numbers.

Given the lack of a clear rule, and common puzzles, let’s consider that this might be a number puzzle where each cell is the sum of its two neighbors in a path.

But without more info, it's hard.

Wait — look at the bottom:

- (5,1) = 3
- (5,2) = 6
- (5,3) = 11

3, 6, 11 — differences: +3, +5

Then (6,2) = 12 — not on the same row.

(6,2) = 12, (6,3) = ? , (6,1) = ?

(7,1) = -2

Now, 3, 6, 11 — perhaps next is 18? But 11 to 18 is +7, so 3,6,11,18 — differences +3,+5,+7 — odd numbers.

But then (6,2) = 12 — not 18.

Alternatively, 3, 6, 11, then 12 — not matching.

Another idea: perhaps the value in a cell is the average of its neighbors.

For example, take cell 0: it has neighbors: 5, 6, 11, 3, 8, 4? — but 8 and 4 are not directly adjacent.

Assume that 0 is adjacent to: 5 (north), 6 (southeast), 3 (southwest), and also to the cells at (3,2), (3,3), (4,2), (4,4)

But we don't know those.

Perhaps the puzzle is to find the number in the cell at the top, which is missing.

But without a clear rule, it's difficult.

Given the time, and since this is a common type, let’s consider that the numbers are part of a sequence where each number is the sum of the two above it.

But not applicable.

Wait — look at the right side:

- (5,3) = 11
- (6,2) = 12
- (7,1) = -2

Is there a relationship between 11, 12, and -2?

11 + 12 = 23, 23 - 25 = -2? Not helpful.

12 - 11 = 1, -2 - 12 = -14

No.

Another idea: perhaps the product of certain cells is constant.

But unlikely.

Perhaps the puzzle is to find the value of the cell at (3,2) or (4,2), etc.

But without more context, it's hard.

Given the difficulty, and since you mentioned "solve the problem", I suspect that the intended solution is that the numbers are placed such that the sum of numbers in each straight line of three cells is constant.

For example, in a hexagonal grid, there are lines in 6 directions.

Let’s assume that.

For instance, consider the line from (3,1)=4 to (4,1)=8 to (5,1)=3 — sum = 4+8+3 = 15

Another line: (4,2)=? to (5,2)=6 to (6,2)=12 — sum = ? +6+12 = ? +18

If sum is 15, then ? = -3

Similarly, (3,2)=? to (4,2)=? to (5,2)=6 — sum = ? + ? +6 = 15 — so ? + ? = 9

But too many unknowns.

Another line: (2,1)=5 to (3,1)=4 to (4,1)=8 — sum = 5+4+8 = 17 — not 15

So not constant.

Another possibility: the sum of all numbers in the grid is zero.

Sum known = 47, so missing sum = -47

But 7 cells, so average -6.7 — possible.

But not helpful.

Perhaps the puzzle is to find the value at the top, and it's a trick.

Or perhaps the answer is 0, but it's already used.

Given the complexity, and since I can't see the image, I must admit that without more context or a clear rule, it's impossible to solve.

However, a common such puzzle is the "hexagonal number puzzle" where the number in each cell is the sum of the two cells above it.

But in this case, it's not a triangle.

Another possibility: the numbers are related to their position in a spiral.

Start from center 0.

Then go clockwise: 6, 11, 12, -2, 3, 8, 4, 5, ...

But 6,11,12,-2 — not increasing.

Perhaps it's a typo, and -2 should be 2.

But not sure.

Given the time, I think the most likely intended solution is that the missing number at the top is 1, or 7, but I can't be sure.

Without the image or the exact task, I can't provide a definitive answer.

Could you please describe the task or what is being asked? For example, "find the missing number", or "what is the value at the top", or "complete the grid".

With that, I can help further.