Here is one two-step incremental Slitherlink puzzle. With ordinary addition, you very probably couldn’t do any better in terms of the number of steps.

What about addition modulo four, though? This means that, on each step, all zeros become ones, all ones become twos, all twos become threes, and all threes are set back to zeros. This way, you might just be able to make an infinite number of steps! (With the same four puzzles repeating over and over, of course.)

When you state the task like this, it isn’t difficult to achieve at all:

So, let us further require that all four puzzles be (preferably, very) different. Is *that *possible? Yes, it is:

And here are the successive increments. First step:

Second step:

Third step:

Advertisements