Visualizing Tsumego

[daal]

In another thread, viewtopic.php?p=27323#p27323/ Bill Spight made an interesting comment about visualizing tsumego:

... the good L&D solvers looked at potential eye points, while the bad solvers looked at where to put stones.

Can some stronger players corroborate this from their personal experience, and can you describe what goes on in your head while you're doing it? (i.e., can you teach me how to do it?)

[Kirby]

Personally, daal, I think that you should just practice a lot of tsumego, and everything will work out from there.

Maybe your eyes will look at spot X at first, but after a lot of practice, maybe you'll automatically adjust to looking at spot Y.

[freegame]

I don't know why this is in a new threat.

In the original one I posted a video I made.
I did a test using gaze tracking software while solving some tsumego.
If you have a webcam you can try it out yourself.
look at the original threat for more info and the link to the video.

[daniel_the_smith]

The points where your eyes look is surely a result of good solving ability and not a cause of it. If forcing your eyes to somehow look at the right place magically improves your reading I will go find a hat and eat it.

My guess is that really good solvers mentally put down groups of stones and not just single stones, which is why they don't look at individual points. There are some joseki I can do that with, but often I end up putting the stones down one at a time to remember who gets sente.

[dfan]

There is a parallel in chess, where weaker players tend to think more in terms of pieces and stronger players tend to think more in terms of squares.

[daal]

The points where your eyes look is surely a result of good solving ability and not a cause of it. If forcing your eyes to somehow look at the right place magically improves your reading I will go find a hat and eat it.

Well, yeah, I know that, and I guess it's obvious that this sort of ability is a matter of experience and talent. I was just thinking that the different way of looking might be indicative of a different thought process, and since the thought process "I plunk a stone here, and he plunks a stone there etc. is inferior, that there might be some sort of corollary, such as "that space is kinda big, but weakness, weakness, hane, squash, squirm, nakade shape, gotcha." I thought maybe someone could articulate it better, but the more I think about it, the harder it seems because it must differ a lot depending on the type of position and the experience of that player with similar positions.

I don't know why this is in a new thread.

In the original one I posted a video I made.
I did a test using gaze tracking software while solving some tsumego.

I guess you are right, sorry about that. I was more curious about the thought process than the eye tracking, and I thought it didn't belong there... oh well. I looked at the video you made, and I suppose it's ridiculously hard to say what you were seeing (there's the matter of peripheral vision) and what you were thinking while seeing it. I am curious though.

[palapiku]

I was just thinking that the different way of looking might be indicative of a different thought process, and since the thought process "I plunk a stone here, and he plunks a stone there etc. is inferior, that there might be some sort of corollary, such as "that space is kinda big, but weakness, weakness, hane, squash, squirm, nakade shape, gotcha."

HermanHiddema's avatar comes to mind.

[Kirby]

The way you describe your thought here makes me think of sports. You can consider basketball, for example. I'm not that great at basketball, and if you compare the way an NBA player dribbles the ball, it's probably a lot more efficient than the way that I do. I'm kind of awkward and clumsy in comparison.

I guess the question becomes, if I want to be a good basketball player, should I first try to imitate how NBA players dribble, and then let my ability follow, or should I focus on my ability first, and let my dribbling skill adapt over time?

I would guess you could improve in either fashion. However, in my experience, people typically start out with the fundamentals when they learn basketball. They use very basic techniques and practice dribbling in a way that might seem awkward in comparison to a pro NBA player.

But I think that most NBA players, early on in their basketball career, started out with the fundamentals - trying something fancy without being at the appropriate skill level may workout, but certainly some pros probably started by using very basic techniques.

So if we draw a comparison to solving go problems, I think that if you keep practicing in a very basic, fundamental fashion - albeit perhaps inefficient or inferior - you will eventually develop the skills necessary to move on to fancier techniques.

[dfan]

One thing worth noting is that a lot of types of tesuji problems (e.g., capturing races, connections, etc.) are mostly about the placement of the stones themselves. So "I go there, he goes there, etc." thinking is totally not wasted in those scenarios.

For life and death problems, everything tends to come down in the end to 1) making two eyes, 2) shortage of liberties issues. (Am I missing anything?) The latter consideration still requires looking carefully at the stones, but the former one is really all about asking yourself "where are my eyes going to be?". Conversely, a lot of killing comes down to internal conversations such as "If he's going to live, his second eye is going to have to be here, which means I need to find a tactical way of preventing it, aha, how about this placement that sets up a shortage of liberties."

[emeraldemon]

Here's something I've been toying with that is somewhat related: Find an easy life and death problem collection. Solve the problem, but remember what sequences you tried and copy them to sgf immediately after you finish.

Here's an example I did, problem 356 in Graded Go Problems for Beginners vol. 3.

$$W White to play
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . X . X X . . . . . . . . . . . . |
$$ | . . X O O O . X . . . . . . . . . . . |
$$ | . . X O . O O X . , . . . . . , . . . |
$$ | . X O . O X O X . . . . . . . . . . . |
$$ | . X . . . X O X . . . . . . . . . . . |
$$ | . . X X . X O X . . . . . . . . . . . |
$$ ---------------------------------------

Click Here To Show Diagram Code

[go]$$W White to play
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . X . X X . . . . . . . . . . . . |
$$ | . . X O O O . X . . . . . . . . . . . |
$$ | . . X O . O O X . , . . . . . , . . . |
$$ | . X O . O X O X . . . . . . . . . . . |
$$ | . X . . . X O X . . . . . . . . . . . |
$$ | . . X X . X O X . . . . . . . . . . . |
$$ ---------------------------------------[/go]

And here's my thought process, which I copied down immediately after solving:

The first sequence I visualized was this:

$$W Failure, 4 connects
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . X . X X . . . . . . . . . . . . |
$$ | . . X O O O . X . . . . . . . . . . . |
$$ | . . X O . O O X . , . . . . . , . . . |
$$ | . X O . O X O X . . . . . . . . . . . |
$$ | . X 5 3 2 X O X . . . . . . . . . . . |
$$ | . 6 X X 1 X O X . . . . . . . . . . . |
$$ ---------------------------------------

Click Here To Show Diagram Code

[go]$$W Failure, 4 connects
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . X . X X . . . . . . . . . . . . |
$$ | . . X O O O . X . . . . . . . . . . . |
$$ | . . X O . O O X . , . . . . . , . . . |
$$ | . X O . O X O X . . . . . . . . . . . |
$$ | . X 5 3 2 X O X . . . . . . . . . . . |
$$ | . 6 X X 1 X O X . . . . . . . . . . . |
$$ ---------------------------------------[/go]

The throw-in is often a natural place to start, but it doesn't work here. Strangely I didn't see black's capture, but realized anyway the eye was false.

Next I ran through a few other moves quickly, starting with the direct atari, which obviously fails:

$$W Fails
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . X . X X . . . . . . . . . . . . |
$$ | . . X O O O . X . . . . . . . . . . . |
$$ | . . X O . O O X . , . . . . . , . . . |
$$ | . X O . O X O X . . . . . . . . . . . |
$$ | . X 4 3 1 X O X . . . . . . . . . . . |
$$ | . . X X 2 X O X . . . . . . . . . . . |
$$ ---------------------------------------

Click Here To Show Diagram Code

[go]$$W Fails
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . X . X X . . . . . . . . . . . . |
$$ | . . X O O O . X . . . . . . . . . . . |
$$ | . . X O . O O X . , . . . . . , . . . |
$$ | . X O . O X O X . . . . . . . . . . . |
$$ | . X 4 3 1 X O X . . . . . . . . . . . |
$$ | . . X X 2 X O X . . . . . . . . . . . |
$$ ---------------------------------------[/go]

So I checked the diagonal, and made a critical mistake. I read this sequence:

$$W Misread
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . X . X X . . . . . . . . . . . . |
$$ | . . X O O O . X . . . . . . . . . . . |
$$ | . . X O . O O X . , . . . . . , . . . |
$$ | . X O . O X O X . . . . . . . . . . . |
$$ | . X 2 1 . X O X . . . . . . . . . . . |
$$ | . . X X . X O X . . . . . . . . . . . |
$$ ---------------------------------------

Click Here To Show Diagram Code

[go]$$W Misread
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . X . X X . . . . . . . . . . . . |
$$ | . . X O O O . X . . . . . . . . . . . |
$$ | . . X O . O O X . , . . . . . , . . . |
$$ | . X O . O X O X . . . . . . . . . . . |
$$ | . X 2 1 . X O X . . . . . . . . . . . |
$$ | . . X X . X O X . . . . . . . . . . . |
$$ ---------------------------------------[/go]

And thought to myself, "false eye, no good". So I moved immediately to this:

$$W Obvious failure
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . X . X X . . . . . . . . . . . . |
$$ | . . X O O O . X . . . . . . . . . . . |
$$ | . . X O . O O X . , . . . . . , . . . |
$$ | . X O . O X O X . . . . . . . . . . . |
$$ | . X 1 2 . X O X . . . . . . . . . . . |
$$ | . . X X . X O X . . . . . . . . . . . |
$$ ---------------------------------------

Click Here To Show Diagram Code

[go]$$W Obvious failure
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . X . X X . . . . . . . . . . . . |
$$ | . . X O O O . X . . . . . . . . . . . |
$$ | . . X O . O O X . , . . . . . , . . . |
$$ | . X O . O X O X . . . . . . . . . . . |
$$ | . X 1 2 . X O X . . . . . . . . . . . |
$$ | . . X X . X O X . . . . . . . . . . . |
$$ ---------------------------------------[/go]

Now in my mind I had tried every move and none of them worked. I panicked for a few seconds, staring at the problem, before I saw the correct answer and my previous mistake:

$$W Misread, corrected
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . X . X X . . . . . . . . . . . . |
$$ | . . X O O O . X . . . . . . . . . . . |
$$ | . . X O . O O X . , . . . . . , . . . |
$$ | . X O . O X O X . . . . . . . . . . . |
$$ | . X 2 1 . X O X . . . . . . . . . . . |
$$ | . . X X 3 X O X . . . . . . . . . . . |
$$ ---------------------------------------

Click Here To Show Diagram Code

[go]$$W Misread, corrected
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . X . X X . . . . . . . . . . . . |
$$ | . . X O O O . X . . . . . . . . . . . |
$$ | . . X O . O O X . , . . . . . , . . . |
$$ | . X O . O X O X . . . . . . . . . . . |
$$ | . X 2 1 . X O X . . . . . . . . . . . |
$$ | . . X X 3 X O X . . . . . . . . . . . |
$$ ---------------------------------------[/go]

Now it's easy to see the snapback, and white lives. The only thing remaining was to check this:

$$W Misread
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . X . X X . . . . . . . . . . . . |
$$ | . . X O O O . X . . . . . . . . . . . |
$$ | . . X O . O O X . , . . . . . , . . . |
$$ | . X O . O X O X . . . . . . . . . . . |
$$ | . X 3 1 5 X O X . . . . . . . . . . . |
$$ | . 4 X X 2 X O X . . . . . . . . . . . |
$$ ---------------------------------------

Click Here To Show Diagram Code

[go]$$W Misread
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . X . X X . . . . . . . . . . . . |
$$ | . . X O O O . X . . . . . . . . . . . |
$$ | . . X O . O O X . , . . . . . , . . . |
$$ | . X O . O X O X . . . . . . . . . . . |
$$ | . X 3 1 5 X O X . . . . . . . . . . . |
$$ | . 4 X X 2 X O X . . . . . . . . . . . |
$$ ---------------------------------------[/go]

black cant play at because of shortage of liberties. My big mistake was not seeing the snapback threat right away.

I feel like this is helpful to me because I can see when I spend a lot of time on wrong variations or miss something. One thing I've picked up is that my reading mistakes often come from stopping too soon, as in the example above. Often a problem is very easy if you pick out the correct first move by intuition. But if you're not sure you can spend a lot of time floundering. The whole sequence took me less than a minute, but it could have taken 10 seconds if I had seen the key piece I didn't see.

[daniel_the_smith]

Interesting exercise...

$$W White to play (4 fills)
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . X . X X . . . . . . . . . . . . |
$$ | . . X O O O . X . . . . . . . . . . . |
$$ | . . X O . O O X . , . . . . . , . . . |
$$ | . X O . O X O X . . . . . . . . . . . |
$$ | . X . 3 2 X O X . . . . . . . . . . . |
$$ | . . X X 1 X O X . . . . . . . . . . . |
$$ ---------------------------------------

Click Here To Show Diagram Code

[go]$$W White to play (4 fills)
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . X . X X . . . . . . . . . . . . |
$$ | . . X O O O . X . . . . . . . . . . . |
$$ | . . X O . O O X . , . . . . . , . . . |
$$ | . X O . O X O X . . . . . . . . . . . |
$$ | . X . 3 2 X O X . . . . . . . . . . . |
$$ | . . X X 1 X O X . . . . . . . . . . . |
$$ ---------------------------------------[/go]

Oh, I can't play 5 where I want to. OK,

$$W White to play (8 @ 5)
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . X . X X . . . . . . . . . . . . |
$$ | . 0 X O O O . X . . . . . . . . . . . |
$$ | . 9 X O . O O X . , . . . . . , . . . |
$$ | . X O 7 O X O X . . . . . . . . . . . |
$$ | . X 3 4 1 X O X . . . . . . . . . . . |
$$ | 6 5 X X 2 X O X . . . . . . . . . . . |
$$ ---------------------------------------

Click Here To Show Diagram Code

[go]$$W White to play (8 @ 5)
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . X . X X . . . . . . . . . . . . |
$$ | . 0 X O O O . X . . . . . . . . . . . |
$$ | . 9 X O . O O X . , . . . . . , . . . |
$$ | . X O 7 O X O X . . . . . . . . . . . |
$$ | . X 3 4 1 X O X . . . . . . . . . . . |
$$ | 6 5 X X 2 X O X . . . . . . . . . . . |
$$ ---------------------------------------[/go]

OK, one liberty short.

$$W White to play
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . X . X X . . . . . . . . . . . . |
$$ | . . X O O O . X . . . . . . . . . . . |
$$ | . . X O . O O X . , . . . . . , . . . |
$$ | . X O . O X O X . . . . . . . . . . . |
$$ | . X 3 1 . X O X . . . . . . . . . . . |
$$ | . . X X 2 X O X . . . . . . . . . . . |
$$ ---------------------------------------

Click Here To Show Diagram Code

[go]$$W White to play
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . X . X X . . . . . . . . . . . . |
$$ | . . X O O O . X . . . . . . . . . . . |
$$ | . . X O . O O X . , . . . . . , . . . |
$$ | . X O . O X O X . . . . . . . . . . . |
$$ | . X 3 1 . X O X . . . . . . . . . . . |
$$ | . . X X 2 X O X . . . . . . . . . . . |
$$ ---------------------------------------[/go]

Ah, there we go, black can't fill.

All that in 15-30 seconds, I didn't time it. Certainly less than a minute. It's worth noting that I only read the first two ones (well, the second one for sure) out because I misidentified the problem-- I thought it was one where you throw in to reduce a liberty on the edge.

[daal]

$$W White to play
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . X . X X . . . . . . . . . . . . |
$$ | . . X O O O . X . . . . . . . . . . . |
$$ | . . X O a O O X . , . . . . . , . . . |
$$ | . X O b O B O X . . . . . . . . . . . |
$$ | . X . . . B O X . . . . . . . . . . . |
$$ | . . X X . B O X . . . . . . . . . . . |
$$ ---------------------------------------

Click Here To Show Diagram Code

[go]$$W White to play
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . X . X X . . . . . . . . . . . . |
$$ | . . X O O O . X . . . . . . . . . . . |
$$ | . . X O a O O X . , . . . . . , . . . |
$$ | . X O b O B O X . . . . . . . . . . . |
$$ | . X . . . B O X . . . . . . . . . . . |
$$ | . . X X . B O X . . . . . . . . . . . |
$$ ---------------------------------------[/go]

But you both thought something like this first, didn't you?

"I have an eye at 'a', so I need to get another - either at 'b' or by capturing the marked black stones (which look a bit short on libs). Can I threaten both, so that if he protects one I get the other?"

[daniel_the_smith]

Actually, no, I don't recall thinking that. Obviously I realized there was an eye at A, but there was nothing verbal going on about it in my head. I start verbally reasoning when I get stuck, not before, I think.

[dfan]

$$W White to play
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . X . X X . . . . . . . . . . . . |
$$ | . . X O O O . X . . . . . . . . . . . |
$$ | . . X O a O O X . , . . . . . , . . . |
$$ | . X O b O B O X . . . . . . . . . . . |
$$ | . X . . . B O X . . . . . . . . . . . |
$$ | . . X X . B O X . . . . . . . . . . . |
$$ ---------------------------------------

Click Here To Show Diagram Code

[go]$$W White to play
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . X . X X . . . . . . . . . . . . |
$$ | . . X O O O . X . . . . . . . . . . . |
$$ | . . X O a O O X . , . . . . . , . . . |
$$ | . X O b O B O X . . . . . . . . . . . |
$$ | . X . . . B O X . . . . . . . . . . . |
$$ | . . X X . B O X . . . . . . . . . . . |
$$ ---------------------------------------[/go]

But you both thought something like this first, didn't you?

"I have an eye at 'a', so I need to get another - either at 'b' or by capturing the marked black stones (which look a bit short on libs). Can I threaten both, so that if he protects one I get the other?"

To be honest, my reasoning went

• Clearly I have to throw in and capture his stones by shortage of liberties, thus gaining more than enough space to live. (Making two discrete eyes didn't even occur to me at this point.)
• Whoops, that doesn't work.
• OK, I have one real eye and one in progress.
• Since I can't capture the three stones, I'm going to have to make that eye while threatening them.
• At that point, the first sequence I tried was the right one.

[Peter Hansmeier]

Here's something I've been toying with that is somewhat related: Find an easy life and death problem collection. Solve the problem, but remember what sequences you tried and copy them to sgf immediately after you finish.

Here's an example I did, problem 356 in Graded Go Problems for Beginners vol. 3.

$$W White to play
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . X . X X . . . . . . . . . . . . |
$$ | . . X O O O . X . . . . . . . . . . . |
$$ | . . X O . O O X . , . . . . . , . . . |
$$ | . X O . O X O X . . . . . . . . . . . |
$$ | . X . . . X O X . . . . . . . . . . . |
$$ | . . X X . X O X . . . . . . . . . . . |
$$ ---------------------------------------

Click Here To Show Diagram Code

[go]$$W White to play
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . X . X X . . . . . . . . . . . . |
$$ | . . X O O O . X . . . . . . . . . . . |
$$ | . . X O . O O X . , . . . . . , . . . |
$$ | . X O . O X O X . . . . . . . . . . . |
$$ | . X . . . X O X . . . . . . . . . . . |
$$ | . . X X . X O X . . . . . . . . . . . |
$$ ---------------------------------------[/go]

My thought process:

The instant I looked at the problem I saw White's one eye, and my eye went straight to d2, in the next instant recongizing that it threatened a snapback. I automatically connected the stones and saw the shortage of liberties that prevented taking away the eye. I thought, "Jackpot!" I restarted with a black atari at c2. My intuition was that nothing could prevent two eyes, but the possibility of a ko made me wary. I confirmed my guess by reading out the variations with the snapback and the capture at d3, stopping as soon as White played e2 to seal the borders. Two eyes! I spent a few seconds changing black's move order to be sure there were no tricks. I got lucky with my first glance.