12-step ladder

1. Reusable idea: To avoid getting lost in Fibonacci, build a short cumulative chart.
2. If the last step is 1, you come from n-1.
3. Let F(n) be the number of ways to climb n steps.

Back to problem
Answer: 233 ways.
Let $F(n)$ be the number of ways to climb $n$ steps.

• If the last step is 1, you come from $n-1$.
• If the last step is 2, you come from $n-2$.

Therefore:

$$ F(n)=F(n-1)+F(n-2),\quad F(1)=1,\ F(2)=2. $$

Ordered calculation up to 12:

So:

$$ F(12)=233. $$

Reusable idea: To avoid getting lost in Fibonacci, build a short cumulative chart.