Puzzle cachers just LOVE Sudoku (although the craze may have passed). Why not? All you have to do is solve a straight-forward Sudoku puzzle, grab the digits, and plug them into the coordinates. Voila: instant puzzle. The dark side is that some people don't want to solve the puzzle. They'd rather run write a computer program and let it fill in the blanks.
If you've been paying attention to my previous puzzles, you'll know that I disapprove of such measures.
This is the beginning of a series of puzzles that have two goals. The first is to confound the programmers and get you to actually solve these the way they are supposed to be solved. The second is to teach some advanced methods for solving Sudoku. If you progress beyond the easy and easy-intermediate stage, you will discover that there is an elegance and poetry to solving Sudoku that goes beyond mere counting and filling in the missing digit.
The first advanced strategy to learn is X-Wing. If you can wrap your head around this method, you'll start to develop ways of thinking that will allow you to pick up the rest of the strategies. X-Wing is not a strategy to enter a digit in the indicated cells but rather a way to eliminate a digit elsewhere on the grid. Often this information will allow you to fill in a different cell and then complete the puzzle.
Consider the following grid: In the first numbered column, all digits are filled in except the yellow/tan cells. Each must contain a 4 or an 8, but we don't know which goes where. In the second column, all digits are again filled in except the yellow/tan squares, each of which must contain a 2 or a 4. Again, we do not which goes where. However, we know one fact for certain: If 4 is in one yellow square, it must be in the other yellow square as well. If the 4 is in one tan square, it must be in the other tan square. Now, remember that It is impossible for more than one 4 to be in the same row. Therefore, even though we cannot place the 4 in the correct square, we know that we cannot place a 4 in any of the cells with an X in them. This information may be enough to solve the puzzle.
Here is a full puzzle, adapted from a computer program that I have. Much of the puzzle has been filled in, but we now hit a wall if we only know basic and intermediate methods. Consider the light/dark blue cells. One set has 5 and 8 as possibilities. The other has 3 and 5. We Don't know what goes where, but we know one thing for certain: If a 5 goes in a light blue cell, it must also go in the other light blue cell. If the 5 goes in a dark blue cell, it must also go in the other dark blue cell. We do not which goes where right now, but we do know one additional fact: There cannot be a 5 in either of the pink cells. That is enough information to solve the rest of the puzzle. (Now you have a 1-3 double in the top row, eliminating the 3 from the upper left pink cell and leaving a 7)
[I freely admit that this is a TERRIBLE example. That's what I get for trying to mix up my sources and not studying this one thoroughly. Thank you to the Davidsons for pointing this out. I'll supply a better example when I get an idle moment.]
Here are the ingredients for spotting an X-Wing.
1. A single digit must be restricted to ONE of TWO squares in a row (or column).
2. The SAME digit must be restricted to ONE of TWO squares in a different row (or column).
3. The potential cells must form the corners of a rectangle.
The name "X-Wing" comes from the typical X pattern formed by each of these corners.
Now for the puzzle! Every X-Wing relies on a single digit. In the first example above, the digit is 4. In the second example, the digit is 5. Here are two Sudoku puzzles. The first one has not one but two X-Wings in it. Let the larger X-Wing digit in the first be Q. Let the smaller digit in the first be R. Let the digit in the second puzzle be S. Then the cache is at N 37 33.ABC W 122 18.DEF. Use the following formulas. If the calculation for B and E is a two digit number, take the final digit.
A = Q
B = Q + S + S
C = S
D = R
E = Q + R
F = S
The first Sudoku is based on a "7 bomb" "difficult" puzzle by Tetsuya Nishio. (Those are his ratings; maximum "bombs" are nine in this particular collection.) I chose this because it is probably the easiest X-Wing to spot that I have ever encountered. By using ghost numbers, you will fill in two digits almost completely around the entire grid. At that point, you will be confronted with not one, but two X-Wings! They are very easy to spot--and you spot them at the same time. Using this information, you will almost immediately fill in two more cells and then the rest of the puzzle. Remember: Q = the larger X-Wing digit and R = The smaller.
The second Sudoku is based on the final puzzle from the first World Sudoku Championship. Will Shortz calls it "satanic." Supposedly, only one person, Jana Tylova, the first place winner, was able to solve it in the alloted fifteen minutes. I'm not sure why. You will find that you are merrily filling in digits without much thought until you come up against one of the most obvious X-Wings that I have ever seen. At that point, it is relatively simple to complete the rest of the puzzle. [I would normally have expected that World Championship finalists would be able to recognize and use an X-Wing "in the wild," but this was in 2005, before many of the harder strategies had been discovered and documented. However, the other puzzles in the final round are either amazingly tedious or unsufferably cute so I shouldn't really act so smug. Besides, I struggled for days on this one before I knew how to spot an X-wing and eventually abandoned it.]
Please remember that I am not doing anything tricky here, although the description may be convoluted and dense. If anythiing is unclear, please let me know. I chose these Sudokus because the X-Wings are pretty obvious and occur very early in the solution. Usually you don't find an X-Wing until late in the puzzle and you have to go searching for it when you discover that you can't do anything else.
One note of caution. One of the intriguing things about Sudoku is that there is often more than one way to solve them. You may use methods that will let you solve these puzzles without using an X-Wing. If so, you have my respect, but you don't have my cache. You have to find an X-Wing in these Sudokus to find the cache.
I fiddled with these diagrams and solved them six-ways-to-Sunday, but I may have missed something. It has happened before. If you notice a mistake or ambiguity, please just send me a gentle note and I'll get things fixed. Happy Puzzling!