[Retros] Two little SPG-challenges

[Noam Elkies]

"Mario Richter" <mri_two at t-online.de> wrote:


> First challenge:

> 

> Can you do better than 'natch' on a 350MHz-PII-machine?

> 

> (natch - with 128MB hash-table - solves 

>  - Pos A in  3min 50s

>  - Pos B in 34min 04s)


"Anders&Margareta" <uddgren at xpress.se> replied:


> For the record: Natch on P4 3 GHz 512 MB 

> A: 1 mn 18.13 s

> B: 10 mn 11.87 s



> not a great diff 


It's a factor-of-3 difference, enough to change my answer to part A
of the "First challenge"...  I found a solution of A in 2-3 minutes,
and a solution of B in about 5.  But that's not a fair comparison,
because Natch is finding a complete list of solutions and I can't claim
to have proved that there are no others.

Mario further writes:


> Second challenge:

> 

> Both proof games contain a rather paradoxical

> element (at least I consider them that way).

> Can you construct longer proof games (not

> necessarily of the "At-Home"-type), which show

> the same element?


I'm not sure what you mean here.  I see different paradoxical elements
in the A and B solutions, both of which have been featured many times
in longer proof games, so can't be the one common element you have in mind.

NDE