Paul put me on to this puzzle. I've spent a little time playing with it and what I write below is expressed many other places on the web. I promise that unless I write a program (like many other people have done) to solve them, this will be my only post on the subject.
These are the rules I have used to successfully solve any puzzle of the level posted in the paper.
The two main ones can be thought of as "Only spot for the number" and "Only number for the spot" or "Hemmed In" and "Only Number" respectively. The other couple work as helpers for the first two by showing that certain numbers are blocked by other less obvious factors.
1) Hemmed In: This is the only place in the region for this number because appearances of the number in intersecting regions and prior solutions (or givens) in the block prevent the number from being placed in any other open place in the region.
2) Only Number: This is the only number that could go in this spot because every other number is already represented in the three container regions (lines and block).
Helpers:
3) That's MY Line: A number cannot be in a line of a block if it must be in that line in another block. An example will help here.
_________________
A |1 | | |
B | |2 3 4| |
C | | | |
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
i ii iii
The number 1 must be in row C in block ii because it is hemmed in by the 1 in row A and the givens in row B. The number 1 cannot be in row C in block iii, because block ii says, "That's my line for 1."
4) Exclusive groups: Unless you have some sort of amazing brain ability and or training this will only be revealed through markup.
The main way this expresses itself is that if two or three spots in the region must have the number then no other spot may have it. You will see that you have two squares in the region where only A and B are possible. If one is A the other must be B and vice versa. Therefore no other square in the region can be A or B. This works at the triple square level for several expressions of exclusive sets ([ABC ABC ABC] [ABC AB AC] [AB AC BC]). Note that these must be the only possibilities in these squares to qualify for the rule.
On the flip side you may find the members of an exclusive group appear only in the set squares and may therefore remove as possiblities any other numbers in those squares. That is, if A and B appear only together and only in two squares in the region, then no other numbers are possible in those squares.
Ex. You can refine [ABCD ABD CD CDE CE] to [AB AB CD CDE CE] from either direction.
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With these, I can create the Heavy Handed Hints for last Friday's Express-News Puzzle:
1 2 3 4 5 6 7 8 9 ___________________ A | |6 | | B | 4 | 8 | 5 | C | 5 1|9 |2 8| ------------------- D | 7|2 9 | 3| E | 9 | | 1 | F |4 | 6 7|9 | ------------------- G |6 8| 9|5 7 | H | 7 | 2 | 9 | I | | 4| | ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯H3-1 H6-1 B3-1 C8-1 D2-1 G9-1 H9-2 C6-2 C1-2 C5-2 E4-1 G2-1 F8-24 F9-2 F3-2 F4-23 The rest are 1's and 2's. Posted to Games and Sport at December 16, 2005 3:10 PM