Puzzle Archive

Knight Moves 3

Place the numbers 1, 2,…, N (for some N) on a subset of the squares below, so that it is possible for a knight to move from 1 to N via a series of legal knight’s moves. Each number inside the grid represents the height of a building located at that square, and we can think of the knight as jumping from rooftop to rooftop on this series of incrementally taller buildings.

A number outside the grid indicates the first (i.e. smallest) number for which the knight was visible looking into the grid in the direction of that row or column. (As shown in the example.)

The answer to this puzzle is the smallest achievable product of the areas of the connected groups of empty squares in the completed grid.