3-1-4 Pi Day Number Challenge | Math = Love - Free Printable

The task is to create expressions using the digits 3, 1, and 4 exactly once each, along with any mathematical symbols or operations, to generate numbers from 1 to 20. Here's how we can solve this problem step by step:

---

Solution:

#### 1 =
$$
1 = 3 - 4 + 1
$$

#### 2 =
$$
2 = \frac{4}{1} - 3
$$

#### 3 =
$$
3 = 3 \times 1^4
$$

#### 4 =
$$
4 = 4 \times 1^3
$$

#### 5 =
$$
5 = 4 + 1^3
$$

#### 6 =
$$
6 = 4 + 3 - 1
$$

#### 7 =
$$
7 = 4 + 3 \times 1
$$

#### 8 =
$$
8 = 4 \times (3 - 1)
$$

#### 9 =
$$
9 = 4 + 3 + 1
$$

#### 10 =
$$
10 = 4 \times 3 - 1!
$$

#### 11 =
$$
11 = 4 \times 3 - 1
$$

#### 12 =
$$
12 = 4 \times 3 \times 1
$$

#### 13 =
$$
13 = 4 \times 3 + 1
$$

#### 14 =
$$
14 = 4! - 3 - 1
$$

#### 15 =
$$
15 = 4! - 3 \times 1
$$

#### 16 =
$$
16 = 4! - 3 + 1
$$

#### 17 =
$$
17 = 4! - 3 \div 1
$$

#### 18 =
$$
18 = 4! - 3 + 1!
$$

#### 19 =
$$
19 = 4! - 3 + 1
$$

#### 20 =
$$
20 = 4! + 3 - 1
$$

---

Explanation of Key Operations Used:

1. Basic Arithmetic: Addition (+), subtraction (-), multiplication (×), and division (÷).
2. Exponents: Using powers like \(1^3\) or \(3^1\).
3. Factorials: The factorial operation (!) is used for larger numbers.
4. Order of Operations: Parentheses are used to control the order of operations when necessary.

Final Answer:

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