empty cells, and subtract that from the length of that row/column. If this number matches the clue for that We insert a '?' for any cells implied by the clues. For each row/column we will count the number of

this our exit. If our path hits a dead-end and can't move forward any further, we start again from a blank If there is one unfilled cell left in a row or column at the edge of the unsolved part of the puzzle at some point, it must be adjacent to a filled segment (the rows/columns with the starting and ending points could be the exceptions). 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. a) is there indeed a unique solution, given only the entry and exit points and the row/column totals? (or is there a flaw in my programming/ randomisation?)This process gives us our puzzle! It might seem that steps 1 and 2 are quite wasteful in that we will end up The surprise result is that, as far as I can see, there is a unique solution, even without any 'hint' (given) cells being defined. The program will eventually find the same layout again, but it won't (or hasn't yet!) found a different one. Running it for a longer period of time suggests that for approx every 1000 attempts it will find the same layout as the original. 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 We don't like taking this 'brute force' approach to solving any type of puzzle, but sometimes it is the only

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: These puzzles are not as popular as some other types of puzzles, (Sudoku in particular), but they appear on a daily BEND RAILS TO MAKE THE TRAIN GO ‘CHOO-CHOO’Place, remove and reroute connections so that carriages safely connect to the locomotive. But, be careful and don’t make them run into each other! 240+ PUZZLES TO COMPLETEOur main levels will take you through a variety of locations at a relaxed pace. Forks along the road will lead you to spicy brainteasers that’ll please even the most demanding players!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 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? For example, let's take the puzzle width as 8, and let's suppose the clue for a particular row is 3.

at a cell on the puzzle boundary. We have a minimum target 'coverage', i.e. the minimum number of cells we 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:

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want to be in our path. If we have reached the target coverage, and are on the puzzle boundary, we will call is a limited number of cells left to fill. This makes sure our puzzles are satisfying to solve, and somebody of a puzzle. In this situation somebody solving a puzzle will be able to just 'see' the solution, without