Brian Hinkle's 2x3 problem published two weeks ago, which we've called CV-1, is a deep and difficult setting. ACF Bulletin editor Jim Loy wrote to Brian saying that there are probably a thousand drawing possibilities and it would take a year to unravel. This is surely one of the best 2x3 problems ever published. There is no doubt that the draw is subtle, finely balanced, and relies on moves which at times don't seem intuitive or natural.

It's impossible for us to go into everything in a single column, so we'll just show a couple of options and let you use your computer to work through the many different variations.

When you're done, Brian would like to know what your favorite drawing line might be. Write to him at sbhinkle@charter.net with your comments.

Brian points out three major drawing themes: a line that ends in Payne’s Double Corner Draw, one that ends in Roger’s Draw, and one that ends in Dr. Brown’s Draw (as in Boland's Famous Positions page 19).

Brian elaborates: If Black keeps the man on 12, then Roger’s Draw is needed. If Black advances the man on 12 to 20, then Payne’s Double Corner Draw is in order. Finally, the important transposition into Dr. Brown’s Draw shows why White must start with 4-8* and 8-11*.

Wow!

First, we'll show Brian's chosen solution, the one he thinks best represents the trunk line. The solution is very long, and you may wish to use this animation. Notes were provided by Brian.

1.

...

4-8

Note that the seemingly "obvious" 2-6 (chasing with the king) will lose, as will 2-7.

2.	12-16	8-11
3.	16-19	11-15
4.	19-23	...

Or 19-24 15-10* 24-27 2-6 (chasing with the king is now correct) 9-13 10-14 27-31 6-10 31-27 10-15 27-23; this is the same draw as in Dr. Brown's Famous Positions, p.19, colors reversed.

4.	...	15-18
5.	23-26	18-22
6.	26-31	2-6
7.	9-13	6-10
8.	31-27	10-14
9.	27-23	14-10
10.	23-19	10-14
11.	19-15	22-25
12.	15-11	25-22
13.	11-7	22-25
14.	7-2	25-22

Stopping the Black king with 14-10? might be tempting but it loses by 15. 13-17 10-14 16. 17-21 25-22 17. 2-6 14-18 18. 6-9 18-23 19. 9-13 23-26 20. 5-9 26-23 21. 9-14 23-26 22. 14-17 22-18 23. 17-22 Black Wins.

15.	2-6	14-18
16.	6-9	18-23
17.	9-14	23-26
18.	14-17	22-18
19.	17-21	18-22
20.	21-17	22-18
21.	5-9	26-23
22.	17-14	18-22
23.	14-10	23-18

White has to defend accurately; if 23-26? then 24. 10-15 26-23 25. 9-14 23-26 26. 14-18 22-25 27. 13-17 Black Wins.

24.	10-7	22-25
25.	7-11	25-22
26.	11-16	22-25
27.	16-20	25-22
28.	20-24	22-25
29.	24-27	25-22
30.	27-31	22-25
31.	31-26	25-30
32.	26-31	30-25
33.	31-27	25-22
34.	27-24	22-25
35.	24-19	25-22
36.	19-16	22-25
37.	16-11	25-22
38.	11-7	22-25
39.	7-2	25-22
40.	2-6	22-25
41.	6-1	25-22
42.	1-5	18-23
43.	9-14	23-26
44.	5-1	26-23

Precision play is required: if 26-30? then 45. 1-6 30-26 46. 6-10 26-23 47. 10-15 23-26 48. 14-18 22-25 49. 13-17 Black Wins.

45.	1-6	22-18
46.	6-9	18-22
47.	14-17	22-18
48.	9-6	23-26
49.	6-2	26-30

With the Black king way back on square 2, White must now force the Black piece on 17 into square 21. If 18-22? then 50. 2-7 22-18 51. 7-11 26-30 52. 17-21 18-22 53. 11-15 30-26 54. 15-19 26-30 55. 19-23 22-26 56. 23-18 26-31 57. 13-17 31-26 58. 18-14 26-31 59. 17-22 Black Wins.

50.	2-7	30-25
51.	17-21	25-22
52.	7-11	18-23
53.	11-16	23-27
54.	16-19	27-32
55.	19-23	32-28
56.	23-27	28-32
57.	27-31	32-28
58.	31-27	28-32
59.	27-24	32-28
60.	24-19	28-32
61.	19-15	32-27
62.	15-10	27-23
63.	10-14	23-26
64.	14-10	26-23

Drawn. An example of "one holds two."

Next, we'll show a line that we took from the KingsRow engine, using its 10-piece endgame database. Brian called this one, "The King Goes on a Vacation." An animation can be found here.

1	...	4-8
2.	9-14	8-11
3.	5-9	2-7
4.	14-18	7-10
5.	18-22	11-15
6.	22-25	15-18
7.	25-30	18-23
8.	9-13	10-14
9.	12-16	14-10

Brian comments, "This white king decides that now is a good time to 'go on vacation' because the other king on 23 is doing all of the heavy defensive lifting."

10.	13-17	10-7
11.	17-22	7-3
12.	16-20	23-27
13.	22-25	3-7

The computer here gave 22-26 which no human would likely play.

14.	25-29	7-10
15.	29-25	10-15
16.	25-22	27-32

This has now transposed into the solution of Brian Hinkle's A Walk Through Time from Ed Salot's problem composing contest 39.

17.

22-26

...

20-24 is interesting, hoping for the blunder 32-28? Black Wins. But if White avoids the trap, 20-24 only draws.

17.	...	32-27
18.	26-22	27-32
19.	22-17	...

The computer gives 22-26, leading to repetition, but this is another try.

19.

...

15-11!

Not 15-18, which loses.

20.

17-14

...

The computer gives 17-22.

20.	...	11-15
21.	30-26	32-27
22.	14-9	15-10
23.	26-22	10-15
24.	9-14	15-19
25.	14-18	19-24
26.	18-15	24-28
27.	15-19	28-32
28.	22-18	32-28
29.	19-23	28-32
30.	23-19	32-28

Etc. Drawn. A double corner defense which will work as long as the remaining single Black man can't crown.

There is much, much more to this problem and indeed one could spend a year on it. We'll just copy the line seen in many an advanced math textbook: "The rest is left as an exercise for the reader."

Our thanks to Brian Hinkle for this problem, and to Brian and Jim Loy for much of the analysis.