lf number of steps is 1.

IF number of steps =2
There are two different ways to finish 11,2

If number of steps =3
There are three different ways to finish 111,12,21

If number of steps =4
There are five different ways to finish 1111,112,121,211,22


If number of steps =5
There are eight different ways to finish 11111,1112,1121,1211,2111,122,212,221

If u closely look at the numbers you can find that they are numbers of fibonacci series (1,2,3,5,8...) and 89 is also a fibonacci number.

fibonacci numbers are

0,1,1,2,3,5,8,13...

for 1 step, number of different ways is 1 (3rd fibonacci number)
for 2 steps number of different ways is 2 (4rd fibonacci number)
for 3 steps number of different ways is 3 (5rd fibonacci number)

But it is not easy to calculate 100th fibonacci number manually. I don't think we have a formula in place to find the accurate value of nth fibonacci number.