Free math puzzles in English covering all basic math topics and ... - Free Printable

Let's solve the puzzle step by step using the given equations.

We are given:

1. ○ + △ = 8
2. ○ - △ = 4
3. ☆ + □ = 12
4. ☆ - □ = □
5. □ + □ = ☆

And we need to find the values of:
☆ = ?
○ = ?
□ = ?
△ = ?

---

Step 1: Solve for ○ and △ using equations (1) and (2)

From:
- (1) ○ + △ = 8
- (2) ○ - △ = 4

Add equations (1) and (2):

(○ + △) + (○ - △) = 8 + 4
⇒ 2○ = 12
⇒ ○ = 6

Now substitute ○ = 6 into equation (1):

6 + △ = 8 ⇒ △ = 2

So far:
- ○ = 6
- △ = 2

---

Step 2: Use equations (3), (4), and (5) to find ☆ and □

Equation (3): ☆ + □ = 12
Equation (4): ☆ - □ = □
Equation (5): □ + □ = ☆ → This means ☆ = 2□

Now use equation (5): ☆ = 2□

Substitute into equation (3):

2□ + □ = 12
⇒ 3□ = 12
⇒ □ = 4

Then from equation (5): ☆ = 2 × 4 = 8

Now check equation (4): ☆ - □ = □
Left side: 8 - 4 = 4
Right side: □ = 4 → ✔ Correct

So:
- □ = 4
- ☆ = 8

---

Final Answers:

- ☆ = 8
- ○ = 6
- □ = 4
- △ = 2

Let’s verify all equations:

1. ○ + △ = 6 + 2 = 8 ✔
2. ○ - △ = 6 - 2 = 4 ✔
3. ☆ + □ = 8 + 4 = 12 ✔
4. ☆ - □ = 8 - 4 = 4 = □ ✔
5. □ + □ = 4 + 4 = 8 = ☆ ✔

All equations are satisfied!

---

Final Answer:

$$
\boxed{
\begin{aligned}
☆ &= 8 \\
○ &= 6 \\
□ &= 4 \\
△ &= 2
\end{aligned}
}
$$