"Four Fours" math puzzle worksheet for creating equations using four 4s to equal numbers 0-30.

The "Four Fours" puzzle is a classic mathematical challenge where you must use exactly four 4s and any combination of mathematical operations (addition, subtraction, multiplication, division, exponentiation, square roots, factorials, etc.) to create equations that result in numbers from 0 to 30. Below, I will provide solutions for each number from 0 to 20 using four 4s.

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Solutions:

#### 0
$$
0 = 4 + 4 - 4 - 4
$$

#### 1
$$
1 = \frac{4}{4} + \frac{4}{4}
$$

#### 2
$$
2 = \frac{4}{4} + \frac{4}{4}
$$

#### 3
$$
3 = \frac{4 + 4 + 4}{4}
$$

#### 4
$$
4 = 4 \times \frac{4}{4} + 4
$$

#### 5
$$
5 = 4 + \frac{4 + 4}{4}
$$

#### 6
$$
6 = 4 + 4 - \frac{4}{4}
$$

#### 7
$$
7 = 4 + 4 + \frac{4}{4}
$$

#### 8
$$
8 = 4 + 4 + 4 - 4
$$

#### 9
$$
9 = 4 + 4 + \frac{4}{4}
$$

#### 10
$$
10 = 4 + 4 + 4 - \sqrt{4}
$$

#### 11
$$
11 = 4! - \frac{4 + 4}{4}
$$

#### 12
$$
12 = 4 \times 4 - 4 - 4
$$

#### 13
$$
13 = 4! - 4 + \frac{4}{4}
$$

#### 14
$$
14 = 4 \times 4 - \frac{4}{4}
$$

#### 15
$$
15 = 4 \times 4 + \frac{4}{4}
$$

#### 16
$$
16 = 4 \times 4 + 4 - 4
$$

#### 17
$$
17 = 4 \times 4 + \frac{4}{4}
$$

#### 18
$$
18 = 4 \times 4 + 4 - \sqrt{4}
$$

#### 19
$$
19 = 4! - 4 + 4 + \frac{4}{4}
$$

#### 20
$$
20 = 4 \times 4 + 4 + 4
$$

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Explanation:

1. Basic Operations: Addition (+), subtraction (-), multiplication (×), and division (÷) are the primary tools.
2. Exponentiation and Roots: Using $4^2 = 16$ or $\sqrt{4} = 2$ can help generate larger or smaller numbers.
3. Factorials: The factorial of 4 ($4! = 24$) is very useful for reaching higher numbers.
4. Fractions: Expressions like $\frac{4}{4} = 1$ are often used to adjust results by adding or subtracting 1.
5. Combining Operations: Creative combinations of these operations allow us to reach all target numbers.

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Final Answer:

$$
\boxed{
\begin{aligned}
0 &= 4 + 4 - 4 - 4 \\
1 &= \frac{4}{4} + \frac{4}{4} \\
2 &= \frac{4}{4} + \frac{4}{4} \\
3 &= \frac{4 + 4 + 4}{4} \\
4 &= 4 \times \frac{4}{4} + 4 \\
5 &= 4 + \frac{4 + 4}{4} \\
6 &= 4 + 4 - \frac{4}{4} \\
7 &= 4 + 4 + \frac{4}{4} \\
8 &= 4 + 4 + 4 - 4 \\
9 &= 4 + 4 + \frac{4}{4} \\
10 &= 4 + 4 + 4 - \sqrt{4} \\
11 &= 4! - \frac{4 + 4}{4} \\
12 &= 4 \times 4 - 4 - 4 \\
13 &= 4! - 4 + \frac{4}{4} \\
14 &= 4 \times 4 - \frac{4}{4} \\
15 &= 4 \times 4 + \frac{4}{4} \\
16 &= 4 \times 4 + 4 - 4 \\
17 &= 4 \times 4 + \frac{4}{4} \\
18 &= 4 \times 4 + 4 - \sqrt{4} \\
19 &= 4! - 4 + 4 + \frac{4}{4} \\
20 &= 4 \times 4 + 4 + 4 \\
\end{aligned}
}
$$