The central idea
The board alternates number positions with clue holes. Every complete row and column must contain each value from 1 through the board size exactly once. On the classic 7×7 board, each complete line therefore contains 1 through 7.
You do not type numbers or slide them into an empty cell. Tiles are exchanged in pairs. Drag one tile onto another or select the two tiles with taps. When a tile reaches its correct position, the board marks it so that it becomes a stable anchor for later deductions.
Reading the sum circles
Each clue hole contains a sum and two arrows. The number is the total of the two tiles pointed to by those arrows. If a clue is 10 and one of its two positions is already a correct 4, the other must be 6. That local fact combines with row and column constraints.
Extreme sums are often useful because they allow fewer pairs than central sums. Their strength is contextual, though: a clue that is ambiguous at the start may become decisive as soon as one of its two neighbouring values is fixed.
Finishing is only half the goal
Blupoli generates every board with a known optimum. The minimum is 15 swaps on 7×7, 24 on 9×9, 36 on 11×11 and 66 on 15×15. Every size gives five extra swaps before all stars are lost.
The star rule stays transparent: solving at the optimum keeps all five stars, and every extra swap removes one. Reaching zero star-eligible swaps does not lock the board. You can still finish the puzzle, but without stars.
How the optimum is proved
The generator does not attach an approximate difficulty number and call it a minimum. It constructs the initial position with exactly twice as many incorrect cells as the target number of swaps. Because one arbitrary swap can correct at most two wrong positions, that mismatch count creates a mathematical lower bound.
The generator also stores a set of disjoint tile pairs that solves the board in exactly that many swaps. The lower bound and the constructive solution have the same length, which proves the optimum for that generated start state.
Four sizes, one geometry
Available boards are 7×7, 9×9, 11×11 and 15×15. They are all odd by design. Waffle-style clue holes sit on alternating interior intersections; with an odd dimension, every hole keeps four valid number neighbours and the rule needs no special edge cases.
7×7 is the default and the best place to learn the language. 9×9 and 11×11 increase the number of simultaneous relationships. 15×15 creates a much denser session, introduces two-digit tile values and many more clues while keeping the same underlying mechanic.
Size and difficulty are independent
Easy, Medium, Hard and Expert do not mean small, medium, large and huge. A 15×15 Easy puzzle and a 7×7 Expert puzzle are both valid choices. Size controls information volume; difficulty controls how informative the clues and initial correct anchors are.
Lower difficulties favour less ambiguous clue orientations and useful anchors at intersections that affect both a full row and a full column. Higher difficulties preserve the same optimal move count but demand more cross-referencing between sums, row values and column values.
A reliable solving routine
Start from the tiles already marked correct. For every complete row or column, identify which values are missing. Then inspect the sum clues touching those positions. If a line needs only two values and one of those values is currently sitting in the wrong place inside that same line, you can often eliminate it immediately.
Before executing a swap, try to prove both directions. If A belongs where B currently sits, look for evidence that B also belongs where A sits. Swaps that place two tiles correctly are the main route toward an optimal solve.
When you get stuck
Do not start shuffling at random. Recheck extreme sums first, then complete lines with the most correct positions, then intersection cells that belong to both a full row and a full column. Those intersections propagate information into two directions at once.
The built-in hint reveals the target value of one unresolved position. Its best use is not simply to advance. After reading it, reconstruct the reason: which sum, line constraint or elimination would have produced the same conclusion?
Mobile interaction without changing the puzzle
The interface keeps the board as the dominant element. On phones it remains square and uses nearly all available width. Larger sizes progressively reduce type, gaps and corner radii so the complete geometry stays visible without horizontal overflow.
Dragging feels natural on small and medium boards, while the two-tap interaction remains available everywhere and becomes especially useful on 11×11 and 15×15. Keyboard navigation, ARIA states and reduced-motion support cover non-pointer interaction as well.
Persistence, daily puzzles and progress
Number Waffle uses the same platform contract as other Blupoli Puzzles games. The engine stores only game state: size, difficulty, seed, current tile arrangement and move count. The shared host owns timing, results, progress, streaks and synchronization.
Daily boards are deterministic for their date, size and difficulty. Returning with the same configuration recreates the same puzzle, and an unfinished session can resume without silently changing the target underneath the player.
Achievements that reward clean swaps
Number Waffle also emits game-specific achievement signals. Double Swap recognises a move that fixes both participating tiles. Exact Optimum rewards solving at the proven minimum for the chosen size. Always Forward requires every swap to increase the number of correct positions.
All three reinforce the same habit as the core puzzle: inspect first, move second. A completed grid is good; a short, explainable sequence of swaps is better.
Related puzzles
If you enjoy the line restrictions, Sudoku and Futoshiki use similar elimination habits. KenKen adds arithmetic over regions, while Kakurasu approaches sums from another direction. Number Waffle stands apart because the final placement is executed through physical swaps and every move affects the star score.
A good learning path is 7×7 Easy, then either raise difficulty while keeping the board familiar or increase size while keeping clues generous. Once the grid stops looking like a pile of numbers and starts behaving like a network of constraints, optimal swaps become much easier to see.