As stated in another thread, the relative complexity of a go problem can be approximated by the number of variations you need to go through (width) and the length of longest variation (depth). Relative complexity because it depends on a player's strength: a stronger player will consider fewer candidates and will see earlier what the result of a variation will be. For example, the L-group is probably a complex problem for a novice, while it's an end state of a variation for an experienced player (it's dead).
My favorite app gives me a daily diet of 2 easy problems, 2 medium ones and 2 hard problems. For me, KGS 2d, the easy problems require no reading and can be solved at a glance. The medium ones require a little reading and I occasional fail. The hard problems require considerable reading and I get them wrong fairly often.
Examples:
- Click Here To Show Diagram Code
[go]$$B Easy 1
$$ ----------------------
$$ | . . . . . . . . . .
$$ | O O . . . . . . . .
$$ | X X O O O . . . . .
$$ | . X X X O . . . . .
$$ | 1 a O X O . . . . .
$$ | O . X X O . . . . .
$$ | O X X O . . . . . .
$$ | . O O O . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .[/go]
Today's Easy 1 is ridiculously easy. The primitive move at A doesn't work because of White's obvious answer at
. Playing
instead comes in a split second.
Width: 2. Depth 2.
- Click Here To Show Diagram Code
[go]$$B Easy 2
$$ ----------------------
$$ | . 3 . O X . . . . .
$$ | X 1 O O X . . . . .
$$ | X O X O X . . . . .
$$ | . O 2 X X . . . . .
$$ | O O O . . . . . . .
$$ | . X . X . . . . . .
$$ | . X . . X . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .[/go]
Today's Easy 2 is deceptively easy: it's easy to see what the problem conceiver wants us to see. Again, the plain move (
at
) doesn't work and
does. This time however it requires experience to assess the results of these two variations. In the failed variation, Black can still play
and it may give a beginner a hard time to figure out if this is bent 4 or not (it isn't). In the successful variation, the result is eye against no eye and one has to see the approach liberty giving Black the edge in the capturing race (or read out the whole thing). Depending on how you look at it, width = 2 and depth is 3 or 8.
The problem is harder than the previous problem, even if the number of variations is equal, because this requires more depth of reading and/or a higher level of evaluation.
- Click Here To Show Diagram Code
[go]$$B Medium
$$ ----------------------
$$ | . . . . . . . . . .
$$ | . a X . X . . . . .
$$ | . O O X . . . . . .
$$ | . 2 X O X . . . . .
$$ | . 1 O O X . . . . .
$$ | . 5 3 X O . . . . .
$$ | . O . . O . . . . .
$$ | . . O . . . . . . .
$$ | . . . . . . . . . .[/go]
One of the 2 medium problems is presented here. Again it's fairly easy to know what the composer wants us to do. After 5 moves there's a clear winner in the capturing race, Black 4 against White 3, but it may require additional reading to see that White can't make use of any special properties of the corner.
at
is 1 variation and best for both.
at
or at A can be quickly dismissed. Width is 2 (or 4) and depth is 5 (or 11). The problem is on the easy side of medium.