[Retros] No occupied white square

[Francois Labelle]

On 12/20/2013 10:39 AM, Olli Heimo wrote:

> Unto Heinonen was really surpised when he heard that Francois had done the task in 10.0 moves. We are eager to see the positions.


The two positions will be published in Phénix (2014).


> Meanwhile Unto has thought the theme otherwise. Maximize the number of men left on the board in a sound proofgame ending to the position where all men are on same-coloured squares. Unto has one with 24 men left in 13.0 moves.


Nice. The best I have so far is 23 men in 10.5 moves. Here's the 
frequency distribution in 10.5 moves:

#men, #unique proof games
17 11
18 35
19 85
20 64
21 61
22 18
23 1


>   He will publish it in February-2014 in Tehtäväniekka, unless before that someone breaks his record.


I started a search in 11.0 moves limited to 25+ men to speed it up, but 
progress is very slow. I'll keep you informed.

Before that I did a special search for a proof game in 11.0 moves with 
exactly 24 men and ranks 4 and 5 empty. I didn't find anything, but here 
are two close calls:

1. e3 d6 2. Bc4 Qd7 3. Bxf7+ Kd8 4. Bd5 b6 5. Bxa8 Bb7 6. g3 Bxh1 7. 
Bxh1 Nf6 8. Bc6 Qxc6 9. a3 Qxc2 10. Nc3 Qxc1 11. Qxc1 h6

1. d3 h6 2. Bxh6 g6 3. Bxf8 e6 4. Bc5 c6 5. Bxa7 Qb6 6. f3 Qxg1 7. Bd4 
Qxd4 8. b3 Qxa1 9. h3 Qxb1 10. Qxb1 Na6 11. Kd1 Rh7

Each only have a slight dual
7... h6  11... Nf6

10... Rh7 11... Na6

This should give you guys something to chew on while you wait for the 
sound proof games...

     François


> Noam Elkies kirjoitti 06.12.2013 kello 19:28:

>> Francois Labelle <flab at wismuth.com> writes:

>>

>>> My computer found a unique proof game in 10.0 moves with 21 men all on

>>> white squares, and another unique proof game in 10.0 moves with 21 men

>>> all on black squares. A lovely pair of problems! Both are confirmed by

>>> Euclide.

>>>

>>> Looks like this is computer territory. Sorry Unto!

>>>

>>> Now I'd like to know if Unto is still going to publish his 11.0-move

>>> problem in a magazine, and whether I should publish my 2 problems in a

>>> magazine...

>> I don't see why not.  Heinonen's problem was still the first of its kind

>> (albeit by only a few days thanks to near-instantaneous global

>> communication);

>> and the mechanism is probably different.  And you've already

>>   published some

>> of your earlier computer discoveries in problem magazines, so why

>>   not these?

>>

>> NDE

>>

>> P.S. Is it feasible to compute how many such proof games there are in

>> 10.5 or even 11.0 and beyond?  It would be interesting to see what

>> the range of possibilities is (and how much choice Heinonen had for

>> his 11.0-mover).

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