Questival!

Had a ton of fun with these guys at the Cotopaxi Questival. Gallivanting all over the place and learning new things about Boston.

How to Solve a (Standard) WXYZ-Wing in Sudoku in 10 Steps

This is an assignment for my technical writing class. The goal was to create a set of instructions that break down a complex task into a series of easy to follow steps. If you would like to try it for yourself and offer feedback I have included an unsolved puzzle that you can try at the end of the post. I would certainly appreciate any input you may choose to leave in the comments section.

Advanced Sudoku puzzles can include some very difficult patterns that take a lot of time and effort to learn. One of these patterns is known as a WXYZ-Wing and can be particularly painful to find if you don’t know what to look for. By following the ten steps below you should be able to solve this complex pattern without too much difficulty. 

What Is a WXYZ-Wing?

Note: hover over blue words for definitions.

• Think of it as a family of four unsolved cells, one of which is the pivot.
• Besides the pivot, the other three family members each have only two candidates.
• Family members must share a row, column, or block with the pivot.
• Here is where it gets tricky. Each cell in the family contains some combination of a certain group of four numbers. Two or three of these numbers will already be known because they are included in the pivot, the remaining one or two must be found. For example, if the pivot contained the digits 1, 2, and 3, other family members could be [1,2], [2,3], [1,3], [1,x], [2,x], and [3,x] where x is the fourth unknown digit. This is the most difficult part of finding families and requires some practice. Two examples are shown below, each with the pivot shown in green and the other family members in yellow. 
• Crossed out cells can be family members, but cannot be the pivot.
• Warning: Don't fall into the trap of thinking that every family member must share a digit with the pivot. If the pivot has only two candidates then this might not be the case. However, at least two family members will certainly share a digit with the pivot. 

This family is made up of 2, 3, 5, and 7.

This family is made up of 1, 3, 7, and 8.

Identify Possible “Pivots”

[1] Examine each row, column, and block and in each case look for pairs of cells that share the same two candidates and have no more than two candidates. (For instance, if two cells shared a column and both had only the numbers 4 and 7 as candidates.) Lightly cross these cells out.

"Twin" pairs of cells with only two candidates are crossed out if they share a row, column, or block.

[2] For each block, count the number of unsolved cells that have not been crossed out. If the number is two or fewer, lightly cross out the entire block.

3 blocks remain.

[3] In those blocks that have not been crossed out, pick a cell with two or three candidates and follow steps 4-10 below to see if it is the "pivot." Note: crossed out individual cells cannot be the pivot.

The pivot is in green.

Finding Other Family Members

Using one of the possible pivots you identified in step 3, follow the steps on the next page to find the other three family members. If the answer to any of the questions below is 'no' then the pivot you chose in step 3 was wrong, and you need to start over at step 4 using a different one.

[4] Look in the column, row, and block occupied by the pivot for cells with two candidates.

Cells with two candidates that share a row,
column, or block with the pivot are in cyan.

[5] With the pivot as the first family member, can you make a family of four? Note: at least one family member needs to share the same block as the pivot and at least one needs to share a row or column with the pivot.

Green and yellow highlighting shows the complete family.

[6] "Children" cells will be able to see the pivot and each other. The remaining cell in the family is the "spouse" and although it sees the pivot, it cannot directly see the children (there is a ongoing custody battle). Is there a spouse and two children?

Children are shown in orange, the spouse remains yellow.

[7] Do the pivot and its spouse share one digit that both children lack? Think of the spouse's other digit as “A”.

The pivot and the spouse both contain the
digit 4 as a candidate, but neither child does.

[8] Does at least one of the children also have digit “A”?

The spouse shares the digit 3 with one of the
children but not with the pivot.

[9] In the block with the pivot, is there an unsolved cell or cells which can be seen by all four family members?

The magenta cell is unsolved and seen by all family members.

[10] If you answered 'yes' to all of these questions, then congratulations! You have solved the WXYZ-Wing and can eliminate “A” as a possibility in the unsolved cell(s) which the whole family sees.

You're all done!



Below is an unsolved puzzle that you can print off and use to test the instructions.

First Impression of Bali

Today was our first full day in Bali! We woke up pretty early and had breakfast at the hotel and then we met up with out driver from yesterday and took a long drive to the base of Mt. Batur. There is a lot of Hindu imagery and statues everywhere. Also a lot of Buddhist influence although to a lesser extent. Pretty much everywhere we looked they were selling stone statues of every shape and size. But mostly Hindu god shapes. And also mostly Hindu god sizes.

Anyhow. When we got to the base of the mountain we were immediately accosted by these three guys who were offering to be our guide up to the top. "We'll be fine with no guide, thank you very much" we said. But they insisted. Oh how they insisted! "It is our rule, and you must respect our rules here" they countered. But we were not convinced, everything about these guys just said that they were trying to rip us off. We saw one tourist who had just finished and she had paid 1 million RP for a guide to the top. Obviously none of use were too thrilled about that prospect. So we tried to argue with them but to no avail. We agreed that if they could show us some sort of legitimate proof that we were required to take a guide then we would go. But instead they just kept telling us that it was a rule of the "association" and somehow that was more important than the rule of law.

I asked at a tourist information office if there really was such a rule and the woman there said that we could hike without a guide if we wanted to even though she didn't recommend it. So we decided to just ignore them and go up anyway. No luck there though. They drove up on their scooters and tried to stop us but we just kept walking. Then the head guy drove up ahead and parked his scooter so that it blocked most of the path. Then he stood menacingly in front of it with his arms akimbo. When Jonathan walked up and tried to pass him he shoved him back and then he pulled back his jacket to reveal a knife in his belt which he proceeded to run his hands over threateningly. We thought we would call his bluff and we told him if it was really illegal that he should go ahead and call the cops on us, we didn't mind. Unfortunately he wouldn't do it (obviously) and we didn't have a phone to do it ourselves. So, lacking the means to resolve the conflict by way of the police and being at a disadvantage in the weapons department we backed down and went to leave.

I was all for finding another way up or bushwhacking it past the initial parts of the trail but nobody wanted to do that. We were stubbornly going to abandon the idea completely (this after a three hour drive to get there which only goes to show how angry we were with the whole situation) but Josef really wanted to go so we decided eventually to turn around and go with a different tour guide who was cheaper (slightly) and although probably affiliated with the same odious "association" would at least take the cut that those jerks would've gotten.

Now that I'm done ranting... the hike was really good and as we started to get above the valley floor the views of the lake and other mountains as well as the quaint farming village below were absolutely breathtaking.

Lena was having a hard time because she hadn't eaten for 36 hours due to some bad food poisoning and a stay in the hospital.  I wish she had told us that beforehand and I would've forced her to eat something. Anyway, it was understandably hard going for her and she had to turn around about 80% of the way up. Ben graciously offered to go down with her.

The rest of us pushed on to the top where we got to hike around the rim of the crater and stick our hands in some active vents. The rim was pretty narrow and when the clouds rolled in and covered everything it looked like we were on a long narrow island floating in the sky. Well, eventually we did come down and when we finally got to the bottom we feasted sumptuously on really cheap Tim Tams, the best prepared Ramen noodles I've ever eaten, and fresh mango and pineapple juice.


Afterwards we went and drove to Ubud where we got checked into our hotel and then we went and got dinner on the main street. Dinner was good but not great. Gelato after dinner was great but not exceptional. Bali however, and I assume Indonesia as well, is exceptional and nothing else. It has so much personality. To wit, there are these really highly ornamented stone and wood gates all over the place that all look like they are hiding some sort of secret. I feel like if you went through one of them you would be spirited away to another world. If enchantments exist, Indonesia is a land filled with them.

Malaysia Part Uno:

So I went on this really long trip over Chinese New Year right? Yes, and I although I did an excellent job keeping up on my journal I'd rather spare you the ill effects of information overload. So, if you glance down below you will see the first part of a brief-ish synopsis of my recent vacation in it's natural habitat, my blog that is.

Sample day: 

Another lazy day, the only time we got out of the house was to go buy an iPhone 4S for Jonathan at the mall and to get lunch at the foodcourt. After lunch though there was this really cool Qing dynasty imperial vase that had water in it and if you rubbed your hands on the sides it made a cool ringing sound and the water rippled very captivatingly. This afternoon we played in the pool and tonight we played ticket to ride, ate pizza on the roof, and watched Real Steel.

Other Things We Did:

• Went to the top of the Petronas Towers, the tallest twin towers in the world
• Hiked around Batu Caves
• Visited the Museum of Muslim Art and Architecture which was amazing
• Toured the National Mosque and met the Muslim missionairies
• Ate at a delicious Indian cafeteria in little India
• Played the board game Diplomacy, i.e. the best game ever invented

And here are some pictures from the first part of our trip...

The McKinley's family room

Rooftop terrace where we had pizza

Batu Caves

National mosque, they made us wear
purple robes to cover our shorts

Harbin : Day 4

One of the greatest paradoxes in my life is my undying love for skiing and my reluctance to spend the great deal of money which it unfortunately entails. So yes, there was what was reported to be a fairly decent ski resort about 90 minutes outside of Harbin, but no we didn't decide to fork over the $80 US that it would've cost us to go skiing there for a day. What we did find however was a much smaller (much much much smaller) ski hill just on the outskirts of town that was so cheap it was almost free. Not only was it really cheap but the service was great too. They had people who would do your boots up for you! That's pretty awesome. Sadly the ski hill consisted of a single bunny run and a rope tow. On the other hand, it was Gatsby's first time ever skiing so the situation was pretty ideal for giving beginning ski lessons. It was pretty difficult trying to teach someone to ski in Chinese but eventually I figured out the right set of vocabulary and all in all it was a pretty enjoyable way to spend the morning.

After skiing we went and grabbed some noodles by the train station and then boarded our long and painful train ride home. This time we had two seats in the hard sleeper car and two seats in the regular car. The three guys took turns sleeping in the bed and sitting in the cheap seats. It is hard to imagine how painful it would be to have purchased a "standing only" ticket from Harbin to Nanjing.

Harbin : Day 3

If you go far enough north, and stay long enough, it stands to reason that eventually you will be eaten by a polar bear. This seems fairly certain. Thus, we put all the polar bears we can catch in cages and drive gas guzzling cars to fuel global warming so that we can destroy the habitats of the remaining few. Now, if this perfect plan fails to completely mitigate the issue at hand at least we can more easily control who gets eaten by the polar bears and when. And that brings me to day 3 in our adventures to the northern China frontier. We went to Polarland which was this great arctic themed zoo/aquarium thing the highlight of which was the two enormous polar bears that they had. In actuality we never got to see the polar bears eat anything they just swam back and forth, all that stuff about polar bears eating people was just to build suspense. But in some other universe perhaps they feed people to polar bears at the zoo. Maybe convicts or something, I don't know. Well, after the polar land we went to dinner at a Russian restaurant that Gatsby's friend recommended and which we all heartily approved of after we ate there.

walking to polarland

Harbin : Day 2 Part 2

In the afternoon on day two we went and saw the reason that Harbin is famous: the snow and ice festival! It was pretty impressive and lived up to the hype for the most part. It would have been much more enjoyable had I not contracted an incurable case of the hiccups (the kind that hurt) for the last 45 we were there. Because it hadn’t officially opened yet there were some parts that were closed off. I could try and describe all the different sculptures and buildings but that would just unnecessarily drain my literary powers which are not unlimited. So instead I’ll just share the magic of Harbin’s number one tourist attraction through some enlightening pictures.