First of all, you have to write some code to populate this ArrayList before executing the code in the JSP. Otherwise, the list will always be empty and the <logic:iterate> tag will have nothing to iterate over.
Secondly, if you want to have inputs on your form that are used by Struts to automatically populate a bean, the properties you wish to populate must be in the ActionForm bean associated with that page's action. You can't just put an array of objects into some scope and expect Struts to populate them when the form is submitted.
You would need to define the solution List as a property on your ActionForm bean and then define a getter/setter pair for the whole list, and another getter/setter pair to retrieve or set a single element of the list given it's index.
this link will give you some good information about using indexed properties in forms.