About Neutralizator II

Puzzle details

This variant of Neutralizator puzzle adds more particles to both corners, so we start with already cloned 30 particles. If you've seen the origins of this brain teaser you know that three particles in one corner cannot escape: it is impossible to clear that corner only by clonning particles (see why on this video from Numberphile).

Three particles at corner, outer region shadowed.
One type of particles cannot escape white region only by cloning. There will always be at least one particle at the white region!

So, if only by cloning we cannot escape from one corner with 3 particles, we cannot with 15 particles. But this puzzle is solvable because we have two types of particles. The fact that we can destroy some clones reequilibrates the game and makes it solvable. One strategy is, therefore, to cancel some particles near the corners.

Advance with one clone to opposite corner.
One strategy is to advance with one clone and try to annihilate as much opposite particles as you can before clonning opposite elements.

The minimal solution for an nxn Neutralizator puzzle are 6(n-2) steps (when n > 2). But this puzzle is not as simple and requires more moves. I don't know the optimal but it could probably be calculated with a computer search. If you manage to do so, I will be very interested in the results.

Advance in rows or columns cloning the same particle.
An example of a possible strategy for solving the brain teaser.




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