[Retros] Mushikui Reconstruction

Mu-Tsun Tsai tsai39 at illinois.edu
Fri May 20 09:48:38 EDT 2011

Dear retro friends,

Today I would like to propose a (perhaps new) type of game reconstruction
stipulation, inspired by the HAP problem by Mark Tilford and the
"mushikuizan" puzzle. I call it "mushikui reconstruction". Thanks to
Mr.Brobecker and Mr.Yeh for their trial on my sample compositions and their
encouragement for me to post my results here on RML.

[I] Introduction

The idea of mushikui reconstruction is the following. A score of a chess
game, written in PGN format, is presented. However all the characters are
concealed by "*" symbols, so that only the length of the representation of
each move is known to the solvers. For example "Qxd2+" will become "*****",
and "cxd6ep" will become "******", etc. The task for the solver is, of
course, to recover the entire game score based solely on these informations.
Needless to say, the problem needs to have a unique solution.

Here's an (relatively) easy example.

Problem (1): recover the following mushikui score:
1.** ** 2.**** **** 3.** ***** 4.** ***** 5. **** ** 6. ****** **** 7. *****

This problem is considerably easy and I encourage everybody to give it a try
before look at the solution (which is at the end of this message).

[II] My compositions

The solutions for the problems in this section are not given in this
message. Feel free to email me if you need them.

Problem (2): recover the following mushikui score:
1.** ** 2.**** ** 3.****** **** 4.** ***** 5.** **** 6.**** ***** 7.****
****

This one is still pretty easy.

----

Problem (3): recover the following mushikui score:
1. ** ** 2. **** **** 3. **** **** 4. *** **** 5. *** ***** 6. **** ***** 7.
****

This one is a bit tricky (in my opinion), but still not so hard.

----

Problem (4): recover the following mushikui score:
1. ** ** 2. **** **** 3. **** **** 4. *** ***** 5. **** ** 6. ** **** 7. ***
***** 8. **** **** 9. *** **** 10. ***** ***** 11. *** ***** 12. ****

This one is perhaps the toughest one in this message (tougher than the next
one!).

----

Problem (5): recover the following mushikui score:
1.*** ** 2.**** **** 3.*** **** 4.**** ***** 5.**** *** 6.***** **** 7.**
*** 8.*** ***** 9.*** **** 10.*** ***** 11.***** ** 12.**** **** 13.*****
**** 14.***** *** 15.***** *** 16. *** ** 17.***** ** 18.***** *** 19.**
***** 20.**** **** 21.*** ** 22.** ***** 23.**** **** 24.*** ***** 25.****
** 26.*** **** 27.** **** 28.** **** 29.*** ** 30.**** **** 31.*** **** 0-1
The game ends with Black mating White.

Here I think putting a "0-1" at the end is enough to indicate the ending of
this game, but still I write the last sentence just to avoid the idea that
White might have just resigned.

I strongly encourage everybody to try this one before reading further
(because I will expose a big secret to this one later!).

[III] Some theories

Of course, I wrote a program to check the uniqueness of the solution to all
the problems above. Using the same program, I also examine all the possible
mushikui sequences up to six single moves. Among them, only two will force a
unique solution:

1.*** ** 2.**** ****, whose solution is 1.Nc3 d5 2.Nxd5 Qxd5, and

1.** ** 2.**** **** 3.**** ****, whose solution is 1.e4 d5 2.exd5 Qxd5
3.Bb5+ Qxb5.

My elementary program is not fast enough for me to examine all the sequences
with seven single moves or more. I will leave this part as on open question
to you.

In my opinion, I think a problem of this type is more enjoyable when it
consists of a lot of intermediate stages, with each stage having a unique
solution on its own. For example, Problem (5) above can actually be
decomposed as follows:

1.*** ** 2.**** ****
3.*** **** 4.**** *****
5.**** *** 6.*****
6...****
7.** *** 8.*** *****
9.*** **** 10.*** ***** 11.*****
11...** 12.**** ****
13.*****
13...**** 14.*****
14...*** 15.*****
15...*** 16. *** ** 17.***** **
18.*****
18...*** 19.** ***** 20.**** ****
21.*** ** 22.** *****
23.**** ****
24.*** *****
25.****
25...** 26.*** ****
27.** ****
28.** ****
29.*** ** 30.**** **** 31.*** **** 0-1

In this decomposition, the end of each line represents an intermediate stage
that has a unique solution. Totally it has 21 intermediate stages and 62
single moves, so I shall define its "intermediate stage density" to be
21/62. The portion of this problem up to move 28. has intermediate stage
density 20/56, which is higher than 21/62. Another open quest I will leave
here is to construct a problem with the highest intermediate stage density!

[IV] Some open quests

Here I shall propose several open quests (including the ones mentioned
above) for everybody. In the following, by "sequence" I mean a mushikui
sequences with a unique solution.

1. Determine all the sequences with seven single moves, eight single moves,
etc.
2. Find a sequence with the highest intermediate stage density.
3. Find a shortest sequence that has a O-O move in its solution.
4. Find a shortest sequence such that the first move of one side is a
one-step pawn move.
5. Find a shortest sequence with the Valladao theme.
6. Find a shortest sequence with a consecutive ** ******, but it is not an
en passant capture.

In quest 3 through 6, the "length" of a sequence could mean one of the
following: number of single moves, or number of stars "*".

[V] Appendix

Solution to Problem (1): 1.d4 c5 2.dxc5 Qa5+ 3.b4 Qxb4+ 4.c3 Qxc3+ 5.Nxc3 b5
6.cxb6ep axb6 7.Qxd7+

Thanks to everybody for reading this! I hope you all enjoy my compositions,