[Retros] Add pieces

[afretro]

Dear friends,
What’s all the fuss about?

> I think it would be difficult to compose a problem in which it is 

> not possible to add an additional piece (although not impossible).

Any position with closed balances would do. E.g. 7k/7p/P6p/P6p/P6p/P6p/P7/K: no piece can be added. All missing pieces were captured by pawns.
Or should the phrase “(although not impossible)” be taken to mean that it refers to positions with non-closed balances?
Yours,
Andrey


12.03.2011, 09:18, "Noam Elkies" <elkies at math.harvard.edu>:

> Theodore Hwa <hwatheod at cs.stanford.edu>; writes:

>

>>>  it would be difficult to compose a problem in which it is not

>>>  possible to add an additional piece (although not impossible).

>>  Here's one possibility with 30 units, nobody in check:

>>  Starting from the initial position, remove the queens,

>>  and move the kings over to the queens' original squares.

>>  It is not possible to add any pieces.

>

> Neat.  Possibly reducible to 28: move each King one square further,

> removing the Bc1 and Bc8.  Or even 26, going back to T.Hwa's position

> but putting a2,h2,a7,h7 on b3,g3,b6,g6 and removing all four Knights

> (or some suitable combination of Knights and Rooks).  26 could then

> also be attained by a mixture of the two techniques: put the Kings

> back on c1 and c8, and play only h2xg3 and h7xg6; or put just wK on c1

> and add a7xb6.

>

> NDE

>

> P.S. Take the above with a grain of salt since it's well past my normal

> bedtime here...

>

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