Logic Masters Deutschland e.V.

This is my response to Scojo's setting prompt for the week: Killers, Parity Lines and Negators.

The puzzle has been featured by Zetamath - many thanks to him for the feature! During his solve, he struggles to internalise upwards as being a "positive" vertical movement, as he is used to the Sudoku notation system in which row numbers increase as they go down. I commented that I would make a flipped version of the grid as we thought it wouldn't change the logic, only realising as the stream ended that it would in fact affect the vectors that need to be read from top to bottom.

For me, considering upwards to be positive feels less unnatural than reading a vector from bottom to top, so I haven't made the flipped version of the grid, but if I do use this ruleset again - which I'd like to because it gave rise to some fun deductions, and using a different line type may open up new possibilities - I will endeavour to make all vectors read from left to right, then release two versions according to your vertical movement preferences!



Place the digits -4 to 4 once each into every row, column and box. [For the answer check to work, write negative digits as regular positive digits]

Digits in a cage must sum to the indicated total, if given.

Draw a loop in the grid, which is a parity line, i.e. digits on the loop alternate between even and odd. The loop must not enter the same cell twice.

Nine cells in the grid are defined as a 'vertex': one in each row/column/box. The loop must pass through every vertex.

Every cage is a 'vector' in the form (x,y), read from left to right or top to bottom. A vector shows that, from the vertex in its box, the loop travels x cells rightwards, then y cells upwards, then arrives at another vertex.