Fill each region with the digits 1 though N, where N is the number of cells in the given region. For every cell in the grid, if K denotes the number in that cell, then the nearest value of K (looking only horizontally or vertically) must be located exactly K cells away. (As in the example, below.) Some of the cells have already been filled in.
Once the grid is completed, take the largest “horizontally concatenated number” from each region and compute the sum of these values. Enter this sum as your answer. Good luck!