1. **State the problem:** We need to find how many odd numbers are there between 16 and 80. 2. **Understand the problem:** Odd numbers are integers that are not divisible by 2. We want to count all odd numbers $n$ such that $16 < n < 80$. 3. **Identify the first and last odd numbers in the range:** - The first odd number greater than 16 is 17. - The last odd number less than 80 is 79. 4. **Use the formula for counting terms in an arithmetic sequence:** Odd numbers form an arithmetic sequence with common difference $d=2$. The number of terms $N$ between first term $a_1$ and last term $a_N$ is given by: $$N = \frac{a_N - a_1}{d} + 1$$ 5. **Apply the formula:** $$N = \frac{79 - 17}{2} + 1 = \frac{62}{2} + 1 = 31 + 1 = 32$$ 6. **Conclusion:** There are 32 odd numbers between 16 and 80.