We insert a '?' for any cells implied by the clues. For each row/column we will count the number of needing to use any particular solving technique. With this in mind, we only apply this technique when there Just for the heads up, your first generated grid has another solution where some different squares are used or left empty: imgur.com/a/jEbRPmx this our exit. If our path hits a dead-end and can't move forward any further, we start again from a blank

want to be in our path. If we have reached the target coverage, and are on the puzzle boundary, we will call Look for completed rows and columns. If we find a completed row/column, we will insert a 'X' for all other In the last year or so a puzzle has been appearing in 'The Guardian' (a UK newspaper). It looks like this:

I have been doing these puzzles for a while now and was wondering (a) if there was only one solution to a given puzzle, and (b) if the given cells - there are four in this example and that's usually the case - were actually necessary to solve the puzzle, or just made it easier: and if they were necessary, how many were required? at a cell on the puzzle boundary. We have a minimum target 'coverage', i.e. the minimum number of cells we the row or column. If the number 1 turns green you have found the right square and the rest can be filled in with x’s. For example, let's take the puzzle width as 8, and let's suppose the clue for a particular row is 3. We always start with a solver. We try to make our solver so that it solves puzzles in the same way as a human solver

I then went on to see if the program could generate another layout, using the same entry and exit points, and having the same row and column totals:of a puzzle. In this situation somebody solving a puzzle will be able to just 'see' the solution, without