The second Akron Beacon Journal CREATORS of 3/15/22 Sudoku turned out to be a good one for comparing Sysudoku bypass solving without 3,4-fills, with 3-fills only, and with every resolvable 4-fill. Scroll back to see the givens grid above.
My bypass trace without fills, goes through values 1 through 7 with little follow through. Then the action is in values 8 and 9.
All three comparison traces reach the solution shown later.
Want to spot the hidden dublex Chdx9 that begins the last leg? If you played it out and are into 3-fills, you might have noticed how many you were passing up.
With 3-fills, the solution is reached on one value, 3. It’s interesting how 3 – 9 clues and subsets generated by dublexes and cross hatches are now produced by 3-fills. This shows how 3-fills add basic solution pathways, and why harder puzzles provide fewer 3-fills.
The 3-fill trace goes on to the final solution.
As you might expect, 4-fills add more pathways to the basic solution. Since 4-fills resolve less frequently, I normally include a 4-fill in the trace only when it immediately resolves. Most of these occur because a missing value sees two or three 4-fill cells in its box. You will probably spot the exceptional case of three cells in separate boxes seeing the same value as you look for the missing value confirming the normal case.
You could do otherwise, but I normally resolve givens 3 and 4 fills before starting the 1 – 9 value list. It’s because n-fill follow up is a more systematic procedure, requiring less searching. Here, as in the all 3-fill case, we don’t get around to that list.
All three traces end with the same candidate combinations that account for the difficulty of the puzzle. The 3-fill trace ends on a 3 value leg, but both the no n-fill and 4-fill end with the same hidden dublex.
My problem with doing 3 and 4-fills exhaustively is overlooking the start of a new one. I’ve lost a lot of time going back to overlooked 3 and 4-fills on blog puzzles to be published. When you this happens in ordinary solving, you very seldom need to go back looking for an extra solution path. Unless, of course, your oversight is caught by a fellow Sysudokie you compete with by sharing traces.
Coming next in this 4-fill clinic is Akron Beacon Journal Gold CREATORS of 3/30/22. Starting off normally in the values list, a clue revealing a 4-fill is actually a missing value in a 5-fill that resolves to the 4-fill. Actually looking for 5-fills isn’t worth the time.