A type of logic puzzle of my own invention. The app generates random puzzles using recursive backtracking, and can also visualize the solving algorithm.

This type of puzzle is best compared to Sudoku; the game has a consistent set of rules, but the number of possible puzzles is immense.

You can use the app to play through some puzzles yourself, or you can have the app solve the puzzles for you. You can visit the app here.

The game consists of a 5 x 5 grid. Each of the 25 squares represents a logical statement about some of the other statements on the grid. Furthermore, each of these statements is either true or false, and the goal of the puzzle is to find all of the statements that are true.

Each statement consists of a directional arrow (up, down, left, or right), a number (0 - 4), and a letter (T or F).

The directional arrow indicates which statement(s) the current statement is making a claim about. An up arrow, for instance, indicates that the statement in question is making a claim about all the statements that are above and in the same column as the statement in question. Similarly, a left arrow indicates that the current statement is making a claim about the statements that are to the left of and in the same row as the statement in question.

The number and letter indicate how many statement(s) allegedly meet a specific truth value (True or False). A statement which reads "2F", for instance, is claiming that exactly 2 statements in the indicated direction are false. Likewise, a statement which reads “0T” is claiming that exactly 0 statements in the indicated direction are true.

Keep in mind that every statement can be either true or false. Therefore, while a statement that reads “3T” is claiming that exactly 3 statements in the indicated direction are true, that statement could actually be false! If it were the case that only 2 (or 4, or 1, or 0) statements in the indicated direction were true, for instance, then you should evaluate the statement as being false.

Your objective is to find all the statements that are true and mark them with the color green. You can select a highlighter color from the palette just below the game board, and you can click on any grid square to mark it with the selected color. All the colors other than green are unnecessary, but you can use them to take notes if you wish. The built-in solver uses the red color to mark false statements, but this is entirely optional. A puzzle is considered to be solved when all of the true statements and none of the false statements are marked in green.

This app generates and solves puzzles using a recursive backtracking algorithm. The algorithm incrementally adds one piece of information at a time, and removes a piece of information if at any point it fails to satisfy the requirements of the problem.

The solver moves through each statement one by one, and first assumes that the statement is false. Provided that this assumption does not violate any of the rules of the puzzle, the solver moves on to the next statement and makes the same assumption. When assuming a statement is false inevitably violates the rules of the puzzle, the solver instead assumes that the most recent statement it looked at is true. If this also fails to produce a valid solution, the solver returns to the previous statement, and assumes that it is true instead of false. This process repeats until the solver finds the correct solution.

The puzzle generator works through a similar method. It first begins with a 5 x 5 array of true and false values. Then, it replaces each value one by one with a condition consisting of a direction, a number, and a boolean value. After replacing each value, the generator runs the solver to ensure that the puzzle still has only one solution. If it has more than one solution, the algorithm backtracks. Unfortunately, these algorithms run with an exponential time complexity. The generator may produce a valid puzzle in a fraction of a second, or it may take over an hour to complete. Keep this in mind if you are using the generator; you may have to refresh the page if it is taking too long. The solver, at worst, will only take a few minutes if you get unlucky.

You can read more about backtracking algorithms here.

This project was built with the React.js library, and was initialized with Create React App. Admittedly, I think that Create React App is somewhat dated at this point, and future projects of this kind will most likely be built with Vite.

I also made use of web workers in this project to ensure that the UI does not freeze when the program is generating a puzzle.

There are a few improvements I’d consider making in the future.

• Using Webassembly would speed up the puzzle generation algorithm.
• Including the “T” and “F” in each square is actually superfluous; I could simply include a number that indicates how many true statements are in the designated direction.