## Discussion Forum

### Daily Magic Spell Discussion - January 2, 2017

Daily Magic Spell Discussion - January 2, 2017

Today, we will discuss about the Daily Magic Spell problem given on January 2, 2017:

Problem: Find the value of $\displaystyle \frac{20!-19!}{18!}$.

Solution: Note that

$\displaystyle \frac{20!-19!}{18!} = \frac{20(19!) - 19!}{18!} = \frac{19(19!)}{18!} = 19\times 19 = 361$.

Some students may attempt to evaluate $20!$, $19!$, and $18!$ naively. Although this could yield the correct answer, the approach itself requires too much effort to solve the problem.

If you have any other approaches that you would like to share with us, feel free to post and let us know how you would tackle this problem! We would like to hear your thoughts!