Maximum size and minimum no. of clues?

[singzeon]

Hi all.

On Puzzle Baron and other logic puzzle websites / apps, so far it looks like 3x4 is the smallest grid and 4x7 is the largest. I was just wondering: has there ever been a 5x4 grid? Is there a maximum size to the grid one can have? And for each grid size, is there a minimum no. of clues for it to be playable?

[boxeeboxeebox]

There is no theoretical limit to the size of a logic puzzle, but beyond a certain number of variables, you veer into "work" territory, either because using a grid becomes unwieldy, or because solving requires too much comparison of the type "the remaining possibilities for X are not valid for Y therefore X does not equal Y", which becomes harder with more variables. If you look at a print puzzle book, you'll find puzzles where you don't get a working grid (like you would on this site), just an answer grid.

As for number of clues, it depends on how many pieces of information are in each clue. So a clue that is "X is not Y" is one piece of information ("X is not Y"), but "X is bigger than Y" is four pieces of information (X is not Y, X is not the smallest value, Y is not the biggest value, X is bigger than Y). You'd need at least (X-1)*Y pieces of information to solve a grid.