2024 Challenge: Yearly Number Challenge | Math = Love - Free Printable

The task is to create mathematical expressions using the digits \(2, 0, 2,\) and \(4\) exactly once each, along with any mathematical symbols or operations, to generate numbers from 1 to 30. Below are the solutions for each number:

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Solutions:

#### 1
\[ 1 = \frac{2 + 0}{2} + 4 - 4 \]

#### 2
\[ 2 = 2 + 0 \times 2 \times 4 \]

#### 3
\[ 3 = \frac{2 + 0 + 2}{4} + 4 \]

#### 4
\[ 4 = 2 \times 0 + 2 + 4 \]

#### 5
\[ 5 = 2 + 0 + 2 + \sqrt{4} \]

#### 6
\[ 6 = 2 \times 0 + 2 + 4 \]

#### 7
\[ 7 = 2 + 0 + 2 + 4 \]

#### 8
\[ 8 = (2 + 0) \times 2 + 4 \]

#### 9
\[ 9 = 2 + 0! + 2 + 4 \]
(Note: \(0! = 1\))

#### 10
\[ 10 = 2 \times 0 + 2 \times 4 + 2 \]

#### 11
\[ 11 = 2 + 0! + 2 + 4! \]
(Note: \(4! = 24\), so \(0! + 2 + 24 = 27\), but we need a simpler approach)
\[ 11 = 2 + 0 + 2 + 4! / 2 \]

#### 12
\[ 12 = 2 \times 0 + 2 \times 4 + 2 \]

#### 13
\[ 13 = 2 + 0! + 2 + 4! / 2 \]

#### 14
\[ 14 = 2 \times 0 + 2 \times 4 + 2 \]

#### 15
\[ 15 = 2 + 0! + 2 + 4! / 2 \]

#### 16
\[ 16 = 2^4 + 0 \times 2 \]

#### 17
\[ 17 = 2^4 + 0! + 2 \]

#### 18
\[ 18 = 2 \times (0 + 2 + 4) \]

#### 19
\[ 19 = 2^4 + 0! + 2 + 2 \]

#### 20
\[ 20 = 2 \times (0 + 2 + 4) + 2 \]

#### 21
\[ 21 = 2^4 + 0! + 2 + 2 + 2 \]

#### 22
\[ 22 = 2 \times (0 + 2 + 4) + 2 \]

#### 23
\[ 23 = 2^4 + 0! + 2 + 2 + 2 + 2 \]

#### 24
\[ 24 = 2 \times 2 \times (4 + 0!) \]

#### 25
\[ 25 = 2^4 + 0! + 2 + 2 + 2 + 2 + 2 \]

#### 26
\[ 26 = 2 \times (0 + 2 + 4) + 2 \]

#### 27
\[ 27 = 2^4 + 0! + 2 + 2 + 2 + 2 + 2 + 2 \]

#### 28
\[ 28 = 2 \times (0 + 2 + 4) + 2 \]

#### 29
\[ 29 = 2^4 + 0! + 2 + 2 + 2 + 2 + 2 + 2 + 2 \]

#### 30
\[ 30 = 2 \times (0 + 2 + 4) + 2 \]

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Final Answer:

\[
\boxed{
\begin{array}{ll}
1 = \frac{2 + 0}{2} + 4 - 4 & 16 = 2^4 + 0 \times 2 \\
2 = 2 + 0 \times 2 \times 4 & 17 = 2^4 + 0! + 2 \\
3 = \frac{2 + 0 + 2}{4} + 4 & 18 = 2 \times (0 + 2 + 4) \\
4 = 2 \times 0 + 2 + 4 & 19 = 2^4 + 0! + 2 + 2 \\
5 = 2 + 0 + 2 + \sqrt{4} & 20 = 2 \times (0 + 2 + 4) + 2 \\
6 = 2 \times 0 + 2 + 4 & 21 = 2^4 + 0! + 2 + 2 + 2 \\
7 = 2 + 0 + 2 + 4 & 22 = 2 \times (0 + 2 + 4) + 2 \\
8 = (2 + 0) \times 2 + 4 & 23 = 2^4 + 0! + 2 + 2 + 2 + 2 \\
9 = 2 + 0! + 2 + 4 & 24 = 2 \times 2 \times (4 + 0!) \\
10 = 2 \times 0 + 2 \times 4 + 2 & 25 = 2^4 + 0! + 2 + 2 + 2 + 2 + 2 \\
11 = 2 + 0! + 2 + 4! / 2 & 26 = 2 \times (0 + 2 + 4) + 2 \\
12 = 2 \times 0 + 2 \times 4 + 2 & 27 = 2^4 + 0! + 2 + 2 + 2 + 2 + 2 + 2 \\
13 = 2 + 0! + 2 + 4! / 2 & 28 = 2 \times (0 + 2 + 4) + 2 \\
14 = 2 \times 0 + 2 \times 4 + 2 & 29 = 2^4 + 0! + 2 + 2 + 2 + 2 + 2 + 2 + 2 \\
15 = 2 + 0! + 2 + 4! / 2 & 30 = 2 \times (0 + 2 + 4) + 2 \\
\end{array}
}
\]