1. **Stating the problem:** We want to find how to get the numbers 4, 30, 36, 52, and 57 from 119 using only ones and twos. 2. **Understanding the problem:** Using ones and twos means we want to express each target number as a sum of 1s and 2s. 3. **General formula:** Any number $n$ can be expressed as $n = 2a + 1b$ where $a,b \geq 0$ are integers. 4. **Finding the combinations:** - For 4: $4 = 2 \times 2 + 1 \times 0$ - For 30: $30 = 2 \times 15 + 1 \times 0$ - For 36: $36 = 2 \times 18 + 1 \times 0$ - For 52: $52 = 2 \times 26 + 1 \times 0$ - For 57: $57 = 2 \times 28 + 1 \times 1$ 5. **Explanation:** We use as many twos as possible, then add ones if needed to reach the exact number. 6. **Relation to 119:** Since 119 is larger than all these numbers, you can think of these as parts or sums less than 119, but the problem only asks how to get these numbers from ones and twos, not necessarily summing to 119. **Final answer:** - 4 = $2 \times 2 + 1 \times 0$ - 30 = $2 \times 15 + 1 \times 0$ - 36 = $2 \times 18 + 1 \times 0$ - 52 = $2 \times 26 + 1 \times 0$ - 57 = $2 \times 28 + 1 \times 1$