sum of the hidden objects in the partitions must be equal to the total number of objects hidden on the board. One possible way to determine a partitioning is to choose the lead clue cells which have no common neighbors. The cells outside of the red transparent zones in Figure 5 must be empty. In other words, there are no hidden objects in the all-white cells. Since there must be a hidden object within the upper partition zone, the third row from top shouldn't contain a hidden object. This leads to the fact that the two variable cells on the bottom row around the clue cell must have hidden objects. The rest of the solution is straightforward. Use of try-and-check method At some cases, the player can set a variable cell as 1 and check if any inconsistency occurs. The example in Figure 6 shows an inconsistency check. The cell marked with an hidden object Δ is under the test. Its marking leads to the set all the variables (grayed cells) to be 0. This follows the inconsistency. The clue cell marked red with value 1 does not have any remaining neighbor that can include a hidden object. Therefore, the cell under the test must not include a hidden object. In algebraic form we have two equations: a + b + c + d = 1 a + b + c + d + e + f + g = 1 Here a, b, c, and d correspond to the top four grayed cells in Figure 6. The cell with Δ is represented by the variable f, and the other two grayed cells are marked as e and g. If we set f = 1, then a = 0, b = 0, c = 0, d = 0, e = 0, g = 0. The first equation above will have the left hand side equal to 0 while the right hand side has 1. A contradiction. Try-and-check may need to be applied consequently in more than one step on some puzzles in order to reach a conclusion. This is equivalent to binary search algorithm to eliminate possible paths which lead to inconsistency. Complexity Because of binary variables, the equation set for the solution does not possess linearity property. In other words, the rank of the equation matrix may not always address the right complexity. The complexity of this class of