"Puzzle Time: Solve the sea-themed multiplication puzzle by finding the value of each symbol."

Let’s solve this step by step.

We are told this is a multiplication table. That means:

> The value in each box = (row symbol) × (column symbol)

The rows and columns are labeled with symbols or numbers. Let’s list them clearly.

---

Step 1: Label the rows and columns

Looking at the grid:

Columns (top row, left to right):
- Column 1: “2”
- Column 2: Shell 🐚
- Column 3: Seal 🦭

Rows (left side, top to bottom):
- Row 1: Shell 🐚
- Row 2: Fish 🐠
- Row 3: “9”

So the grid looks like this:

```
| 2 | Shell | Seal
----------|--------|---------|-------
Shell | Fish | 9 | Jellyfish
Fish |Jellyfish| Manatee | 24
9 |Manatee | Penguin | 36
```

Wait — actually, looking again: the *inside* of the grid has symbols too! But those are the results of multiplying row × column.

Actually, re-reading the directions:
> “Find the value of each symbol in the multiplication table.”

That means: Each cell contains the product of its row header and column header.

But some cells have symbols instead of numbers — that means those symbols represent unknown values we need to find.

Wait — no! Actually, let me reinterpret.

Looking carefully:

The headers (outside the grid) are:
- Top: 2, Shell, Seal
- Left: Shell, Fish, 9

And inside the 3x3 grid, each cell shows either:
- A number (like 9, 24, 36), OR
- A symbol (like fish, jellyfish, manatee, penguin)

BUT — the instruction says: “Find the value of each symbol in the multiplication table.”

Ah! So the symbols INSIDE the grid are not headers — they are placeholders for products? No, that doesn’t make sense.

Wait — perhaps I misread.

Let me look again.

Actually, here's the correct interpretation:

This is a multiplication table where:

- The row labels (on the left) are: Shell, Fish, 9
- The column labels (on top) are: 2, Shell, Seal

Then, each cell inside should be: (row label) × (column label)

But in the grid, some cells show numbers (which are the actual products), and some show symbols — which must mean those symbols represent the PRODUCT of their row and column.

Wait — but then why are there symbols like "fish" inside the grid? That would be confusing.

Alternative interpretation (more likely):

The symbols inside the grid are NOT products — they are VARIABLES representing unknown values. And the numbers given (9, 24, 36) are known products.

But that contradicts the direction: “Find the value of each symbol in the multiplication table.”

Another possibility: The entire grid is filled with products, and the symbols shown inside are just illustrations — but that can't be, because then we wouldn’t know what to solve for.

Wait — let’s read the directions again:

> Directions: Find the value of each symbol in the multiplication table.

And below the grid, there are boxes next to symbols: Shell, Seal, Jellyfish, Fish, Penguin, Manatee — so these are the symbols whose values we need to find.

Also, note: In the grid, some cells contain numbers (9, 24, 36), and others contain symbols (fish, jellyfish, manatee, penguin). Those symbols inside the grid are probably meant to represent the same symbols as the ones we’re solving for — meaning, when you see “fish” in a cell, it means the product equals the value of the “fish” symbol.

But that seems circular.

Wait — here’s the key insight:

In a multiplication table, if row A and column B intersect, the cell = A × B.

Here, the row and column headers include both numbers and symbols.

So, for example:

Cell at Row=Shell, Column=2 → should be Shell × 2

But in the grid, that cell shows a FISH symbol.

That suggests: Fish = Shell × 2

Similarly, Cell at Row=Shell, Column=Shell → shows 9 → so Shell × Shell = 9 → Shell² = 9 → Shell = 3

Oh! That makes sense!

Let’s formalize:

Define variables:

Let S = value of Shell 🐚
Let F = value of Fish 🐠
Let J = value of Jellyfish 🎐
Let M = value of Manatee 🐄 (or whatever that sea cow is)
Let P = value of Penguin 🐧
Let Se = value of Seal 🦭

Now, from the grid:

Grid positions (row, column):

Row 1: Shell (S)
Row 2: Fish (F)
Row 3: 9

Column 1: 2
Column 2: Shell (S)
Column 3: Seal (Se)

Now fill in the grid with equations:

Cell (1,1): Row=Shell, Col=2 → S × 2 = ? → but grid shows FISH → so:
→ F = S × 2 ...(eq1)

Cell (1,2): Row=Shell, Col=Shell → S × S = 9 →
→ S² = 9 → S = 3 (since values are positive) ...(eq2)

Cell (1,3): Row=Shell, Col=Seal → S × Se = ? → grid shows JELLYFISH →
→ J = S × Se ...(eq3)

Cell (2,1): Row=Fish, Col=2 → F × 2 = ? → grid shows JELLYFISH →
→ J = F × 2 ...(eq4)

Cell (2,2): Row=Fish, Col=Shell → F × S = ? → grid shows MANATEE →
→ M = F × S ...(eq5)

Cell (2,3): Row=Fish, Col=Seal → F × Se = 24 →
→ F × Se = 24 ...(eq6)

Cell (3,1): Row=9, Col=2 → 9 × 2 = 18 → but grid shows MANATEE →
→ M = 18 ...(eq7)

Cell (3,2): Row=9, Col=Shell → 9 × S = ? → grid shows PENGUIN →
→ P = 9 × S ...(eq8)

Cell (3,3): Row=9, Col=Seal → 9 × Se = 36 →
→ 9 × Se = 36 → Se = 4 ...(eq9)

Great! Now we can solve step by step.

From eq2: S² = 9 → S = 3

From eq9: 9 × Se = 36 → Se = 4

From eq1: F = S × 2 = 3 × 2 = 6

From eq6: F × Se = 6 × 4 = 24 → matches given → good check.

From eq7: M = 18 (given directly from 9×2)

Check eq5: M = F × S = 6 × 3 = 18 → matches → good.

From eq8: P = 9 × S = 9 × 3 = 27

From eq3: J = S × Se = 3 × 4 = 12

From eq4: J = F × 2 = 6 × 2 = 12 → matches → perfect.

So now we have all values:

- Shell (S) = 3
- Seal (Se) = 4
- Jellyfish (J) = 12
- Fish (F) = 6
- Penguin (P) = 27
- Manatee (M) = 18

Now, the question asks to fill in the boxes at the bottom:

They show:

[ ] → Shell → 3
[ ] → Seal → 4
[ ] → Jellyfish → 12
🐠 [ ] → Fish → 6
🐧 [ ] → Penguin → 27
🐄 [ ] → Manatee → 18

(Note: The last one is drawn like a manatee or dugong — we called it Manatee.)

All values are consistent and verified.

Final Answer:

Shell: 3
Seal: 4
Jellyfish: 12
Fish: 6
Penguin: 27
Manatee: 18

──────────────────────────────────────

Final Answer:
Shell = 3, Seal = 4, Jellyfish = 12, Fish = 6, Penguin = 27, Manatee = 18