## Task B-2.3.

There are 8 steps to the top of the staircase. In how many ways can we reach the top if we can climb by one step or by two steps?
## Solution.

On the $k$-th column $(k \geqslant 3)$, we can reach it in one step from the $k-1$. or $k-2$. column.

1 point

This means that the number of ways to reach the $k$-th column is equal to the sum of the number of ways to reach the $k-1$. column and the $k-2$. column.

We can reach the 1st column in 1 way, and the 2nd column in 2 ways.

We continue by the principle of addition:
on the 3rd column
$1+2=3$ ways,
on the 4th column
$2+3=5$ ways,
on the 5th column $3+5=8$ ways,
on the 6th column 13 ways,
on the 7th column 21 ways,
on the 8th column 34 ways.