Bricks, like Sudoku, is a type of latin square puzzle. All latin square puzzles use the same broad template:
Start with an NxN square grid.
Fill in cells with digits from 1 to N.
Don’t repeat numbers in any row or column.
Beyond that, each variant of a latin square puzzle has its own special requirements to give it a unique feel. For a Bricks puzzle, this involves the 1×2 “bricks” subdividing the grid.
Fill in the grid with the numbers 1 to N (N being the length of a side), without repeating a digit in any row or column.
Each 1×2 “brick” contains one odd and one even number.
If the dimensions of the grid are even (6×6, 8×8, etc), half-bricks at each end of a row are considered one brick.
Otherwise, half-bricks are simply a digit not used elsewhere in the row.
Basic Techniques to Solve
In Bricks puzzles, the techniques tend to work together in such a way that it’s impractical to give examples without using a whole grid. This time, I’m just going to summarize the tips, and we’ll go straight into solving our example puzzle.
Prioritize rows and columns with more known numbers.
Use the even/odd requirement of whole bricks to narrow down candidates. Note that in any odd-sized wall (9×9, 7×7, etc), the half-bricks at the ends will always be odd.
Cross-reference with multiple rows/columns to find a number position in one row/column.
Marking candidates is a powerful tool.
Solving the Puzzle
In Sudoku puzzles, you would normally start by scanning along a row or column of a given number to find its position in one of the 3×3 regions. Because Bricks puzzles don’t have these regions, those methods don’t help, and it can be difficult to find where to start. That’s why priority one is always to look for rows and columns that have the most given numbers. Ideally, you want them to be mostly even, or mostly odd.
Fill the grid with the numbers 1-9 so that there are no duplicates in any large triangle region or any of the three possible rows for each cell. Rows are considered to cross the gap.
“All in all, it’s just another brick in the wall.” On this day in 1979, Pink Floyd released one of their most well-known concept albums. The Wall sold over 30 million copies. Today, we celebrate with a Bricks puzzle.
Fill in the grid with the numbers 1-9 such that there are no duplicates in any row, column, or 3×3 region. Inequality symbols between adjacent cells indicate which cell has the greater number.
Mathrax originated on the German puzzle website janko.at. Fill in numbers from 1 to 9, such that no row or column contains any duplicate numbers. Sounds pretty normal so far, right? Now let’s add math!
You’re the coordinator for this year’s Secret Santa party. Each of your seven guests brought a present for each of the others. You mixed in the gifts from you, and arranged them in a neat grid, with one present for each guest in each row and column. No idea why – you just liked the arrangement. But then the labels fell off of most of them! Fortunately, you were able to remember a bit about how they were arranged. Can you deduce the rest of the labels?