Can you toggle the cell-colors by mouse-clicks
such that all numbers are zero? This problem has been shown to be NP-complete [2].
In this problem there are two colors (not counting white indicating an empty cell). However for a single color the problem is easy [5] and can be solved in time O(n log n), where n is the side length of the grid. The first NP-completness proof for a constant number of colors was [4]. |
Can you drag the dominoes on the grid such that all the numbers become zero? This problem has been solved in 2007 by Nicolas Thiant in his PhD who gave a polynomial time algorithm for it, for the case the dominoes have to tile completely the grid. Otherwise the problem is NP-complete [1]. |
Can you select cells of the grid with the mouse such that (1) all number are zero and (2) the convex hull (in red) contains only selected cells? This is an open problem. However if as additional contraints you have projection number from two other particular directions then the solution is unique and can be computed in polynomial time as shown by Alain Daurat [2 and 8] . |