I really enjoyed the special 19x19 and 21x21 puzzles and have done all the 17x17s in the books (including one without pencil marks!) Got me thinking: what's the largest puzzle that can be made that would still be practical and playable? By practical I mean that the "free squares" would be kept to a minimum so that the puzzle would still be challenging. Would 25x25 be within practical limits of computing power? How about 100x100?
The solving time required goes up a lot for each increase in dimension (i.e. adding 1).
For 25x25 I'd need some major improvements in the solver, and/or only do puzzles that have many smaller cages (max 3 cells for example).
100x100 is too far out I think (but if someone has any ideas, let me know )
ddarthez
Posted on: Thu Aug 12, 2021 7:48 am
Posts: 82 Joined: Fri Jan 13, 2017 2:51 pm
Re: How large can the puzzles realistically get?
Think that would really depend on what numbers you use. For example, multiples of say 14641 are easy to work with, since they must contain 4 times the number 11. Same with other primes (other than 2, 3 and 5 for 25x25), since their squares will not be in the puzzles. Also extreme sums (for example a sum of 6 in 3 cells, in a straight line), can make things a bit easier. You also can't construct a puzzle where too much is straightforward. There is no challenge in too many of numbers like 14641, or 4913 etc.
The bigger the puzzles get, the more hints must actually be contained (implicitly) in the numbers you get to solve the cages. In general, required time for a human solver will increase exponentially when adding another dimension, so unless you give a lot of 1-cell cages, the realistic maximum for humans would be in the 25x25 to 30x30 range. Adding in operators like squares, mods or doing things with say the numbers -12 to +12 (inclusive of 0), is pushing it then even for the best human solvers.
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