In 2014, I wrote a number of Spontaneous Saturday articles about Conceptis Puzzles (June 14, August 12, and August 30). Recently (i.e., two weeks ago), contrary to my expectations, Conceptis came out with a new type of puzzle: Cross-a-Pix.
Cross-a-Pix is a picture logic puzzle (like Fill-a-Pix and Pic-a-Pix) which, while it looks like another form of B/W Pic-a-Pix, is actually radically different from any other puzzle of its kind. In this particular type of puzzle, you have multiple regions of differing shapes and sizes that you either fill in or mark blank, depending on the clues. Cross-a-Pix comes in two forms: Single Clue and Double Clue.
Like the name implies, Single Clue Cross-a-Pix puzzles have only one number as a clue to a row or column. For these types of puzzles, you have to consider the following:
- Small and large numbers. For large numbers, if you have a region (or a tile set) of a length greater than N – n, where N is the number of tiles left in the row or column and n is the number represented by the clue, the region must be highlighted. Similarly, for small numbers, if you have a region of length greater than n, where n is the number represented by the clue, the region must be marked blank (although this goes without saying). In our example, the 8 and 2 (both on rows) are the clues of interest. 4 > (10 – 8) and 3 > 2, so:
- The number of tiles remaining in a row or column. As you work through the puzzle, consider the regions you have and haven’t highlighted. In this case, look at the row marked with a 7. Because the L-shaped region has been marked blank thanks to our previous rule, the row now has 9 spaces left. This means the 3-space region can be marked like so:
- Completed rows and columns. I know this goes without saying, but pay attention to rows and columns that have already been completed, like the column marked with a 2. As you can see, that one already has 2 marked tiles, so we can mark the rest blank, like so:
- The patterns of a row or column. This factor is where a bit more thinking is involved. Look at the fifth column from the left, the one marked with a 6, the rightmost of two adjacent 6s. If you look closely, there’s no way to complete the column without highlighting any of the 2-space regions. This seems more like a complex version of factor 2, but nonetheless, it is something to note. Our example can now become:
Taking all of the following into consideration, if you complete the example correctly, it should look like this: http://i.gyazo.com/46cacf0465705a382e181a1a1556b0ad.png (posted as a link for fear of spoilers)
In Double Clue Cross-a-Pix, the clues are marked with two numbers instead of one. The first number (leftmost in a row, uppermost in a column) represents the number of squares to be filled, while the second number (rightmost in a row, lowermost in a column) represents the number of groups into which the filled-in squares must be divided. Thus, the criteria to consider while completing these puzzles are quite a bit different:
- Clue numbers that are close to each other. In a row or column, if a region takes up a number of spaces greater than (a – b + 1), where “a” is the first clue and “b” is the second clue, it must be marked blank. Knowing this, our example can be marked as follows:
Using the formula, the 2 2 column and row, as well as the 3 3 row, cannot contain any regions that take up any more than 1 space (2 – 2 + 1 = 1; 3 – 3 + 1 = 1); and the 4 3 column cannot contain any regions that take up more than 2 spaces (4 – 3 + 1 = 2).
- Rows and columns with a second clue number equal to 1. In this case, you have to think about the patterns, similarly to how you’d consider factor 4 of Single Clue. Specifically, start from the beginning and/or the ending tile, and count as many tiles as the first clue. If you happen to end on a tile that is within the region rather than on the end, you must mark blank whatever tile you started on (beginning or ending tile). For instance, if you start on the end of the 6 1 column and go six tiles up, you end up on a tile that is not the end of the region, so you would have to mark blank the last tile in that column, like so:
(the red circle is there to make it easier to tell)
If you keep going through this process, you may just end up whittling a row or column down to the point where there are only just enough tiles in the row or column to support the first clue. (This just so happens to be the case in this example, you see?)
- Unifying and breaking groups of blackened tiles. Here is something to keep in mind when solving Dual Clue Cross-a-Pix: the number of groups in a row or column does NOT constantly increase. For instance, in the 7 3 column, if I were to blacken the 6th tile down, the current number of groups would decrease from 3 to 2 (a concept to which I refer as “unifying”). Now, if I were to do that, there would be no way to increase the number of groups, so that’s a no-no. Instead, you have to mark that tile blank so that the groups are broken rather than unified. Similarly, the black tile in the 2 2 row should be “broken” as well. The result:
The tiles marked blank are circled above. Note that marking blank the tile in the 7 3 column leaves just enough tiles to satisfy the first clue, so I decided to go ahead and fill up the column accordingly. Note also that the converse process is also true; if you find that you have too many groups in a row or column, you might have to blacken a region to unify a set of groups. However, I cannot think of an instance of this scenario in our example, so just take my word for it.
- Once again, the patterns of a row or column, particularly one that already has one or several blackened regions. Let’s skip ahead a little…
Now, look at the lower of the two 4 3 rows. If you were to fill in the 2-space region taking up the middle two tiles, you would have 3 blackened tiles in 1 group, making it impossible to have 4 blackened tiles in 3 groups; therefore, that region must be marked blank, like so:
If you look closely, you’ll also notice by factor 4 of Single Clue that there is no way to complete the 4 3 row without blackening the 4th tile from the left. (If so, good eye!)
Once completed, the example puzzle should look like this: http://i.gyazo.com/ae6de6bdf1abe224f9a591af04f5000f.png (again, posted as a link for fear of spoilers)
Final note: Factors to consider in Single Clue will definitely help in Dual Clue, but not vice versa. I somehow found Dual Clue easier to pick up, but Single Clue is subjectively easier overall. I hope this post has been of use somehow, and y’all have fun solving puzzles!