Place the digits 1–9 exactly once in each row and each column of the grid. Draw a directed path that moves orthogonally between cell centres and visits every cell of the grid exactly once. Each of the 27 cages can be entered by the path at most once (i.e. the path must visit all cells of a cage in a single continuous run before leaving it). The path acts as a thermometer with respect to cage totals: as the path moves away from its starting cell, the sums of the cages it visits must strictly increase. Digits may not repeat within a cage.