Solved at Scale
A Bigger Cost Matrix
A rectangular assignment instance with more workers than tasks keeps the same one-to-one structure but forces an idle worker. The candidate count is a partial permutation, small enough to enumerate exactly here, and the matrix shown is the real data that the external solver reads.
Cost matrix
There are 5 workers and 4 tasks. Why: this is the same one-to-one assignment structure as before, but the matrix is no longer square, so each task still takes exactly one worker while some worker will be left without a task.
One worker sits idle
With 5 workers and only 4 tasks, exactly 1 worker must sit idle. Why: every task takes exactly one worker and a worker takes at most one task, so the workers outnumber the tasks and the extra workers cannot be placed.
Candidate count
Brute force would check 120 candidate assignments here. Why: a candidate injects the 4 tasks into the 5 workers, an ordered pick of distinct workers. The count is small in the pinned example only because the matrix is small; that kind of growth is the reason a method needs more than enumeration.
Diagram note
The table is the exact integer cost data with no assignment highlighted yet; solving comes next. The input boundary is unchanged: costs are exact integers and the objective is their sum over a feasible matching. Pixel positions are rounded for layout; every number shown is exact.