This app was mentioned in 3 comments, with an average of 1.33 upvotes
Boardnaut Studios has previously made some other great app conversions of print and play board games. I would highly suggest checking some of them out if you have not done so. Cheese Chasers is a nice quick fix puzzle/tile game, and the Maquis Board Game is a really great solitaire worker placement game that I have played quite a bit of and still continue to enjoy.
Here are a few actually free, no iap's android digital board games:
Cheese Chasers - a quick 5 min puzzle game, also good on phones: https://play.google.com/store/apps/details?id=org.boardnaut.studios.cheesechasers.android
Land 6 Board Game - https://play.google.com/store/apps/details?id=org.boardnaut.studios.land6.android&hl=en
Word Hero Online - A clone of Boggle, see how many words you can find in a 4x4 grid of letters in 2 mins, then see how you did vs the other 100 or so players who just did the same puzzle. (This one is ad supported by small ads on some score screens): https://play.google.com/store/apps/details?id=com.rhs.wordhero&hl=en
Cheese Chasers might fit the bill.