You'll definitely need arrays. Maths, well not sure about the maths behind it, but you can easily find tutorials / source code for solitaire games.
Yes arrays can be frightening at first, but surely after all these years they shouldn't be scaring you off so much? I do remember you from the CC days ;)
The only way to truly learn arrays is by trying stuff using them.
Simplest way I can think of to learn them is using a 1D array to store hiscores or names, since you'll need to implement sorting. If you can sort through an array, then you can easily shuffle a deck of cards stored in an array.
I'd say a solitaire game would be quite advanced. Don't you have to place them a certain way so that it's not impossible to win? Never attempted it as it never interested me, and I usually don't know the best way to go about things unless I try it.