8x8p12 Daily Calendar Puzzle Design Flaw

We have identified a design flaw in the 8x8p12 Calendar Puzzle. Visually, certain Weekdays lack corresponding answers as there are no appropriately sized puzzle pieces to fill the vacant spaces:

 
With any Month and Date, when Weekday = TUE $ THU

Since this solver design is based on the image of the puzzle which has 12 puzzle pieces, we split 4-cell puzzle piece into 1- cell and 3-cell pieces so that  this solver may  find  solutions for any date with 13 puzzle pieces. Any one has this puzzle on hand, may cut 4-cell piece into 1-cell and 3-cell pieces to play with.