by Guest » Thu Apr 07, 2005 9:12 am
Surprisingly, only two general techniques are required to solve all puzzles published in the times (including fiendish), and often only one is required. I'm not sure if either of these are what you call raising numbers and reaching out.
1) Look for a number (N) of cells in a unit (row, box or column) where only N digits are possible. Each of the N digits can then be eliminated as a possibility from all the other cells. This is just a generalisation of the principle that if a cell has only one possibility then that possibility can't appear anywhere else.
e.g. three cells have the following possibilities (12) (23) (13). This is an "exclusive" set. It doesn't tell us anything about how the digits 1,2 & 3 are placed within those three cells, just that they cannot appear in any of the other cells in the unit.
Note - to cover all possibilities, you need to consider values of N up to one less than number of undecided cells
2) Look for units where the only possible placements for a digit are on the intersection with another unit. In this case, the digit can be eliminated as a possibility from all other cells in the second unit. This is only relevant to the intersections between boxes and rows or boxes and columns.
e.g. All the cells where a digit is possible in box 1 lie on row 3 - That digit can be eliminated from row 3 in boxes 2 & 3.
This second rule is needed less often. Indeed, even Fiendish puzzles can sometimes be solved without it.
These rules developed from designing a solver program, and are very efficient, but unfortunately both techniques (at least the first) really require full pencil marking of the whole puzzle to be effective. I'm trying to get in the habit of doing the puzzles without pencil marks, because it is so much quicker, and can manage now for all but the fiendish ones.
When solving manually I tend to start by seeing which is the most common digit in the clues and placing that digit anywhere obvious, then repeat for all the other digits. I'll keep doing this until nothing is happening. This is often a very rapid way to fill in a lot of cells.
I then look at each unit (starting with the most populated), and see what's missing (so I'll be thinking "1467, 1467", and look at each cell in turn to see if all but one of the possibilities is disallowed by an intersecting unit (so I look along/around the other two units chanting the mantra "1467, 1467"). I normally do boxes first, then rows, then columns (no particular reason). I'll also look for interesting intersections between sparsely populated units, where there are few known digits in common.
For all but the hardest puzzles I generally find that these techniques allow me to solve the puzzles pretty quickly (I can do very easy or easy puzzles in 2-3 minutes) and without pencil marks. I find as soon as I have to do the pencil marks (i.e. when my brain gives out), the solving time plummets, so I might do a difficult puzzle in 5-10 minutes, but a fiendish will take 30-45.