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MatPlus.Net Forum General Longest n-unit directmates?

### Longest n-unit directmates?

I'm in the process of making a length/economy collection of directmate problems. That is, for values of n from 3 upwards, the longest sound n-unit directmate. I'm talking here about problems, not just positions, and thus require at least one full-length solution line with no duals on any White move. In particular, White's key must be unique. "Longest win" positions found using tablebases have their place, but not here.

I've looked in PDB and YACPDB, but so far I have a rather large hole.

At the light end there are:

Bernhard Rittmeier & Hilmar Ebert
Four Men Only 1982A; ZiW, S/1, 1; CPT&R, 742; P1164168
(= 2+1 )

8/8/8/8/8/8/4k1KP/8
#18.5

Bernhard Walter
Die Schwalbe 123, Jun 1990, p. 236, no. 7; CPT&R 748; P1171106
(= 3+1 )

8/8/8/8/3k4/B7/7K/1N
#31

Simo Blom; Ilkka Blom
(= 3+2 )

8/8/8/8/k6B/8/8/2NK1n
#43

For 8, at http://chessproblem.net/viewtopic.php?f=7&t=44 I found

Lelo, 1951
(= 4+4 )

3K4/8/1p6/1B6/8/Bpk5/8/b1N
#53

I didn't find this in PDB or YACPDB. The above web page has a solution line with some analysis, but I don't know if the problem has been proved sound.

Once we allow 13 units, we have
Josef Halumbirek
Magyar Sakkvilag, Jun 1930, no. 334; P1182427
(= 2+11 )

8/7p/7p/p6p/p3Q2p/K6p/p1r5/rk6
#112

Truncating the solution line of the above gives a 12-unit #101 and an 11-unit #84. Now how far does Halumbirek's problem cast its shadow over the n-unit categories for lower values of n? How well can we do for n=6, 7, 8, 9, 10?

Is that requirement for a dual-free line too onerous? Would it be better to relax it, while not relaxing it so far as to allow multi-hundred-move tablebase monstrosities with duals galore? Not sure what would be an acceptable compromise. Perhaps a good compromise is to require the line to be dual-free until Black has bare king?

(2) Posted by Hauke Reddmann [Monday, Jun 14, 2021 11:12]

I don't think we should make concessions, but rather
compile the table in triplicate (to have it all in
one place):
- totally dual-free
- has at least one dual-free main line
- the absolute length record

(Ceterum censeo there should be a webpage collecting
*all* construction records)