I think that is very much possible. I assume you are familiar with lists and variables? A basic setup could be:
With the Input command you display a string on the screen (in this case: input, somemore and random) and the answer that the user gives is stored to L₁(#) in which # is a number from one to 'n' as defined in the first line of the code example. The only problem with this is that the user can not input a string, that is a series of alphabetic characters. so the first input (or the last, that does not really matter) can never be "Cow". It has to be numeric. This is because you cant store letters or series of letters to lists, they can only contain numeric values. If you want to store something liek cow and not a numeric value you'll need to replace
There are more effecient ways in which you would not use up all ten strings but at the moment I think that is a little too complicated.
You can recall your input later like this
The last thing I saw in the solver were the buttons on the bottom. For animated buttons like those BASIC is too slow. I'll think you have to devise a other way of affirming that you are done (as a user).
If there are any unclearities don't hesitate to ask me for more thorough explaination. Alot of info can also be found on data types (e.g. matrices, strings, reals etc) on this site! You can also look up the "input" command if you don't understand it.