Pairing Order and Chaos

• Chaos Construction: Divide the grid into seven orthogonally connected seven-cell regions, and place the digits 1-7 once in each row, column, and region.

• Parity Sums: A clue outside the grid gives the sum of all continuously adjacent digits that are alternating in parity up to (and not including) the first digit that repeats parity. For example, the row 1235467 would have a sum clue of 6=1+2+3 from the left (3 and 5 are both odd) and a sum clue of 13=6+7 from the right (4 and 6 are both even).

Moreover, for each clue the digits contributing to its sum must belong to the same region and the first parity-repeating digit must belong to a different region.

• Region Counters: A digit in a square counts how many different regions intersect the indicated row or column (i.e. how many region have at least one cell contained in that row or column).