Number Waffle

What is Number Waffle?

Number Waffle takes the standard waffle swapping mechanic and replaces the letters with numbers. The 7x7 grid needs to satisfy two constraints at once: every row must contain the numbers 1 through 7 with no repeats, and every column must do the same. On top of that, there are clue circles at each intersection. Each circle has a number and two arrows pointing to the neighboring cells in that row and column. Those two cells have to add up to the number shown.

Green tiles are already in the correct position and lock down. You swap the remaining tiles into place using the row, column, and sum constraints together to work out where each number belongs.

Tips for Number Waffle

Start with the sum clues that have extreme values. A circle showing 3 can only be made by 1 and 2. A circle showing 13 can only be 6 and 7. Those pin down two cells at once with no guessing involved, and confirmed cells make every adjacent clue easier to crack.

Use elimination the same way you would in Sudoku. If a row already has six of the seven numbers placed, the missing one fills the last cell automatically. Keep a mental note of which numbers are confirmed in each row and column as you go.

Green tiles give you free information. A green tile in row 3 means that number is taken in row 3 and in its column. Use both of those facts to shrink the possibilities for nearby unsolved cells.

When two sum clues share a tile, that tile has to satisfy both of them. That's a tight constraint and usually gives you the number in that spot outright. Look for shared cells between adjacent clues before trying to reason about cells that only appear in one.

You have a swap budget, so don't rush. Think through a move until you're confident rather than swapping and hoping. A wrong swap in Number Waffle tends to create a chain of new problems in both the affected row and column at the same time.