Logic Masters Deutschland e.V.

Apply the rules of variable Tapasyus (see below).

But note that in this variant the grid is a torus, i. e. the left and right border of the grid as well as the upper and bottom border are connected.

Draw a closed loop into the grid. It must go from the center of one cell to the center of a horizontally or vertically adjacent cell, passing every cell at most one time.

The loop uses every cell with a circle. Circles may be blackened. In white circles the loop keeps straight on but bends in at least one of the adjacent cells (following the loop). In black circles the loop bends but keeps straight on in both adjacent cells.

The loop must not pass cells containing numbers. A number determines how many of the neighbouring cells are used by the loop. These cells must form a group not interrupted by empty cells, but need not to be a contiguous part of the loop. Distinct groups of loop cells around the same numeric cell must be partened by at least one empty cell.