Nice little problem.
Surprisingly he does not make the observation that the numbers he gets in each cell, as worked in his spread sheet, form Pascal's Triangle: https://en.wikipedia.org/wiki/Pascal's_triangle. Which gives one all kind of interesting ways to think about the problem. As people have been doing for 2000 years or more.
These kind of programming puzzles are rather like the questions in maths challenges. The first thing you have to do is pull the problem out of the words the question uses. Those words are often thrown in as a "blinders" to throw you off the scent. As in this example.
The mathematician Po-Shen Loh gives exactly the same advice as this guy, look for different approaches, play with little examples, look for patterns, to kids tackling maths problems.
"Daily Challenge with Po-Shen Loh": https://www.youtube.com/channel/UCf78EJOm4wQ4xXwSS15PuxQ
Po-Shen Loh likes to say that one should not be afraid of maths, it's just "thinking". And so it is with programming.