by ravel » Thu Nov 30, 2006 11:38 am
Had a look at StrmCkr's solution method now. If i understood it right, i would roughly formulate it following:
1. Try to find numbers that would force all numbers of a unit (row, column, box).
2. Test them with singles chains.
2a.If one solves the puzzle (you found a single backdoor), you are finished.
2b.If one leads to a contradiction, eliminate it.
2c.If you get stuck again, repeat the process (-> 1.) from that position.
So if you are lucky, you will find a solution in 1 or 2 steps (even for very hard puzzles). But with some bad luck you only can eliminate numbers that dont help much.
The chances not to get stuck finally with singles chains are good, because all numbers of the starting unit are fixed, when trying them.
[added:]
I dont know, if there are (real) grids, where you cant find a number to start with. I remember that Gurth once did something similar, he started with a number which obviously fixed the same number in all units. In general each number is a good candidate, that can be seen to fix many cells immediately. Out of those candidates i first would try one, which, when eliminated, would give a number (especially bivalue/bilocation numbers).