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A 6×6 logic puzzle of shading and sums. Every row and column has exactly two shaded squares and the numbers 1 to 4, and each clue outside the grid tells you the sum of the numbers trapped between that line's two shaded squares. One solution per board, reached by logic alone — race the clock.
The board is a 6×6 grid with a clue above every column and to the left of every row. In each row and in each column you must shade exactly two squares and fill the other four with the numbers 1, 2, 3 and 4, each used once.
Each clue is the sum of the numbers that lie between the two shaded squares of its line. If the two shaded squares touch, nothing lies between them and the clue is 0. If they sit at both ends of the line, all four numbers are between them and the clue is 10, the largest possible. Numbers outside the shaded pair do not count. A few squares may start already filled in gold — shaded or numbered — and cannot be changed.
Press Start and the clock begins. Tap a square to select it, then tap the striped shade button or a number on the pad. Tapping the same choice again clears it, and ⌫ erases the square. Turn on Notes to jot small pencil marks for 1 to 4 instead. When you place a number, it is removed automatically from the notes in the same row and column.
The clues react as you work. When both shaded squares of a line are in place and every square between them is filled, the clue turns green if the sum matches. It turns red, together with the squares of that line, if the sum is wrong, if a line has three shaded squares, or if a number repeats. The puzzle is complete the moment every square is filled and all twelve clues are satisfied.
Your score is the time you took, and lower is better. The clock is real time, so it keeps running if you switch apps. Your best time is kept on this device, and you can save any finished time to the Hall of Fame. On a keyboard you can type 1–4, use X, 0 or Space to shade, the arrow keys to move, Backspace to erase and N to toggle notes.
Start with the extreme clues, because they fix the shape of a line. A 10 means both ends are shaded and all four numbers sit between them. A 0 means the two shaded squares touch. A 9 can only be 2+3+4, so exactly three squares lie between the shaded pair and the 1 is outside it. A 1 or a 2 means a single square between them holding exactly that number, and an 8 can only be 1+3+4.
The middle clues have two readings, and listing them is the main technique. A 3 is either a lone 3 or 1+2; a 4 is a lone 4 or 1+3; a 5 is 1+4 or 2+3; a 6 is 2+4 or 1+2+3; a 7 is 3+4 or 1+2+4. Each reading fixes how far apart the shaded squares are, and each distance leaves only a few places for the pair in a six-square line. When a line's options all share a square — for example, when three squares lie between the pair, the two middle squares of the line are always between them and must be numbers — you can often mark something before you know the whole line.
Cross the rows with the columns. Every column also needs exactly two shaded squares, so once a column has both of its shaded squares, every other square in it is a number. That in turn limits where the shaded squares of the crossing rows can go. Use the notes for the two or three numbers that are still possible in a square; the automatic clean-up removes a number from its row and column as soon as you place it.
Remember what the outside squares are worth. The four numbers in every line always add up to 10, so the numbers outside the shaded pair add up to 10 minus the clue. A clue of 7 means the outside squares hold 3 in total — either a lone 3 or 1 and 2. Doppelblock is German for "double block"; the same puzzle is also published as Between Sums. Every board here is generated with a single solution and checked to be solvable line by line, without guessing.