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 CHESS SOLVINGTournamentsRating lists1-Oct-2020 B P C F  MatPlus.Net Forum Promenade Chess math problem quickie

### Chess math problem quickie

(For large values of chess :-)

Put the 32 men on your half of the chess board.
Now divide the 32 fields in four areas A,B,C,D.

Put one piece in each field of area A, except three fields which stay empty.
Put one piece in each field of area B, except three pieces which go back into the box.
Put three pieces in each field of area C.
Put one piece on every third field of area D.

How large are A,B,C,D?

Hauke

How come I can't do a simple math problem?

Also, do three fields of area B stay empty? If that is true, then three fields of area B stay empty and three pieces go back into the box, so why not just say "Put one piece in each field of area B"? I suppose that "except three pieces which go back into the box" means that area B has at least three fields, which is an extra piece of information. That three pieces go back into the box also has influences on C and D, as you have a total of 29 instead of 32 pieces then for all fields.

So you have:
xa + 3 = A
xb + 3 = B (note that B doesn't talk about three fields, but three pieces, so it also could be xd = B)
xc / 3 = C (C being a full number)
xd = D

xa + xb + xc + xd = 29
A + B + C + D = 32  Unfortunately, there is no single solution.

For example:

A=4(1) B=4(4+3) C=6(18) D=18(6)
A=26(23) B=2(2+3) C=1(3) D=3(1)

the parametric limitations:
A>=3
A+B=4k
D=24-3k
C=8-k MatPlus.Net Forum Promenade Chess math problem quickie