Definitions

Here is a list of all the terms we use in order to solve A-puzzle-a-day:

• There is 1 board.
• There are 43 squares on the board. These squares all have a text, 12 months and the numbers 1 to 31.
• Sometimes we group n×m squares. We will call this a rectangle. 2 more remarks:
• The board itself is a 7×7 rectangle with 6 squares missing at the edges.
•  NOTE: some people may argue that an n×n rectangle should be called a square. They are right, but not on this site. Here a square strictly follows the definition in the previous bullet.
• There are 8 forms, all different in size. 1 form is a 2 by 3 rectangle covering 6 squares. The other 7 forms all cover 5 squares. In separate chapters we will have a closer look at these forms.
• A solution is a situation where all forms are placed on the board. They will cover 6+7×5=41 squares. So the caption is only visible on 43-41=2 squares.
• A pair is combination of 2 squares, more specific: 2 squares that are uncovered in a solution.
  The number of solutions cannot be calculated upfront; if there would be possible, this site would not have existed. Also the number of solutions per pair cannot be calculated. 
  However, the total number of pairs is known: 43×42÷2=903. (I will not explain; see Wikipedia). Pairs can be categorised:
  
• A date is a combination of a month and a number that can be found on the calendar. As you know there are 366 dates.
• An incorrect date is a combination of a month and a number not found on the calendar. There are 6 incorrect dates:
• February 30
• February 31
• April 31
• June 31
• September 31
• November 31
• A double month is combination of 2 months. There are 12×11÷2=66
• A double number is a combination of 2 numbers. There are 31×30÷2=465 of these, more than all other categories together.
• Back to the forms: an orientation is a way to place a form on board. If you place one form on an empty board, you can rotate it 90, 180 or 270 degrees. You can flip over the form and again rotate in 3 ways. All together you now have 8 orientations.
  But only 4 forms have 8 orientations. 3 other forms have only 4 orientations, which can be found in 2 ways. The rectangle can be placed in only 2 ways, portrait and landscape. We will explain this in separate chapters.
  Actually, the orientation is not particularly interesting, but you need it to find the following:
• A position is an actual location of a form on the board. We will discuss this per form in separate chapters.
  For now it is nice to know that there are 961 positions in total. That means, you have 961 ways to place one form of your choice in any location on an empty board.
• On this site we will search for solutions per pair. Before we do so, we will filter the positions.
  Filtered positions cover one or both of the squares of the pair. That means they can never be part of any solution for that pair.
  
  

Everything is now defined, but in separate chapters we will dig deeper in forms, orientations, positions, filtered positions: This is still under construction, pages are missing or under construction

• Explaining forms, orientations and positions using form 1, the 2×3 rectangle
• Explaining filtered positions using form 1, the 2×3 rectangle
• Forms enclosed by a 2×3 rectangle: 4 and 8
• Forms enclosed by a 3×3 rectangle: 2 and 3
• Forms enclosed by a 2×4 rectangle: 5, 6 and 7
• Forms summary
• Form 7
• Form 8