Logic Masters Deutschland e.V.

I recently discovered marty_sears's Liar Cell series and really enjoyed it. It also reminded me of Robot Lines, a constraint I had only seen used in two puzzles. I decided to try combining the two ideas to create a new sudoku, and this puzzle is the result.

Click the image to play the puzzle.

Rules:

Place the digits 1-9 once in each row, column and 3x3 box of the main grid.

LIAR CELLS: Exactly one cell in every row, column and 3x3 box is a liar. A liar has two different numbers: the DIGIT written in the grid and the real VALUE used by the other clues. For every other cell, digit and value are equal.

• The nine liar digits are the numbers 1-9, with no repeats.
• The nine liar values are also the numbers 1-9, with no repeats.

ROBOT LINES: Each blue-grey line has an inspection robot, with its initial stop marked by a red circle. From any inspected cell, its real VALUE gives the exact number of cell-to-cell steps to the next stop. The robot chooses one direction for that move, then may choose either direction again after stopping. It cannot turn around midway through a move or travel beyond an open end. On a closed loop, it continues around the loop as needed.

The inspection ends only after every cell on that robot's line has been visited as a stop exactly once; the final cell's value imposes no further move. A move may pass through earlier stops, but may not end on one. Each robot stays on its own line.

X / V: The real values of two cells separated by an X add to 10; those separated by a V add to 5.

BLACK DOTS: The two real values joined by a black dot have a 1:2 ratio.

WHITE DOTS: The two real values joined by a white dot differ by 1.

Not every qualifying X, V, black dot or white dot is marked.

NOTES: In the blue arrow beside a row, you may note the digit in that row's liar cell. Use the grey-blue circle beside it for the corresponding real value. These notes are optional.