Printl is not so much a game in and of itself but rather a tool to generate mathematical checks that can offer similar information to a regular, online Wordle game, in print form, without an internet connection.
The checks have been designed targetting a standard 8-digit pocket calculator, though they're simple enough to work out by hand if absolutely necessary. Either way, they're difficult or at least tedious to exploit, to find the correct solution based on what the formulas used might reveal.
Printl was designed as a pedagogical tool for Math Education first and foremost. Depending on a student's level of mathematical knowledge, there's a range of topics that could be covered, such as:
- Arithmetic Operators and Order of Operations,
- Prime Numbers and Divisibility,
- Cyphers and Permutations,
- Factoring Polynomials,
- Systems of Linear Equations and Gaussian Elimination
However, it's perfectly serviceable for what it says on the tin! If you run a publication and wish to print a puzzle generated with the help of Printl feel free!
In any case, I'd appreciate if you got in contact about where and how you use it at editorial@albertrg.me
Generating a Printl puzzle begins with generating a substitution cypher with a set of prime numbers keyed to distinct letters of the alphabet, for players to use when checking their guesses.
The product of all numbers in the solution is provided for players to perform a simple divisibility check, which when true indicates the presence of a letter within the solution. Defaulting to only 4 "letters" rather than 5 is a limitation of the targetted "8-digit pocket calculator".
The correct position for a letter may be checked by substituting it into one of 4 or 5 polynomials and checking if it's a root of the polynomial that corresponds to that spot. The polynomial roots are chosen such that each polynomial is a depressed cubic, with all real roots but only one which is available as a guess from the substitution cypher.
To that last point: Another of the roots will always be the index of the row/column being tested (counting from 1), so repeat letters are distinguished, and the third root is chosen to guarantee the quadratic coefficient is 0. This way every puzzle is unique and deterministically determined based on its solution.