How to programmatically solve the 15 (moving numbers) puzzle?

Question

all of you have probably seen the moving number/picture puzzle. The one where you have numbers from 1 to 15 in a 4x4 grid, and are trying to get them from random starting positi

Answer 1

You're definitely on the right track, but rather than solving by row/column iteratively to the point of being left with a 2x2, solve until you have a minimum 3x3 and then solve just that grid. 3x3 is the smallest size you need to properly re-order the grid (while 2x2 doesn't give you the complete flexibility you may need as you've already discussed). This approach is scalable too - you can solve 5x5, 10x10 etc.