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Chess puzzle I found in my dad's old book

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Re: Chess puzzle I found in my dad's old book

#11

Post by dwa3592 »

ra0x3 wrote: post #6

Wait, the instructions are a little ambiguous. I clicked "Solution" and it has the dark-squared bishop on a white square! XD Should maybe update the instructions to clarify that the dark-squared bishop is not constrained to dark squares.

that's exactly what happened to me. I ended up spending so much time thinking black bishop can only go to black squares. and agreed this is a bit ambiguous.

Re: Chess puzzle I found in my dad's old book

#12

Post by NooneAtAll3 »

dllu wrote: post #3

Neat. Surprisingly, there are 388 solutions, and a lot of them look rather unintuitive. ........ ...Q.... ........ ........ .....Q.. ........ ........ Q..B..Q. Q....... ........ ........ ........ ..QQB..Q ........ ........ ........ My original intuition was to place the queens on unique rows and columns to cover as much as possible but it turns out there are solutions with three of them on the same row. Python script…

is there a solution where all the pieces are covered as well?

Re: Chess puzzle I found in my dad's old book

#14

Post by NooneAtAll3 »

ra0x3 wrote: post #6

Wait, the instructions are a little ambiguous. I clicked "Solution" and it has the dark-squared bishop on a white square! XD Should maybe update the instructions to clarify that the dark-squared bishop is not constrained to dark squares.

> The task is to place four black queens and one black bishop on the chessboard

where did you read "dark-squared"?

Re: Chess puzzle I found in my dad's old book

#15

Post by sltkr »

loganc2342 wrote: post #8
ra0x3 wrote: post #6

Wait, the instructions are a little ambiguous. I clicked "Solution" and it has the dark-squared bishop on a white square! XD Should maybe update the instructions to clarify that the dark-squared bishop is not constrained to dark squares.

It's a black bishop, but not necessarily a dark-squared bishop. Both the black side and white side in a normal chess game get a dark-squared and a light-squared bishop, and I don't see anywhere that specifies which type this one is. It can be either one depending on where you place it.

Also if you care that much just mirror the solution horizontally or vertically, and now your bishop is on the white square instead.

Re: Chess puzzle I found in my dad's old book

#16

Post by sobellian »

dllu wrote: post #3

Neat. Surprisingly, there are 388 solutions, and a lot of them look rather unintuitive. ........ ...Q.... ........ ........ .....Q.. ........ ........ Q..B..Q. Q....... ........ ........ ........ ..QQB..Q ........ ........ ........ My original intuition was to place the queens on unique rows and columns to cover as much as possible but it turns out there are solutions with three of them on the same row. Python script…

I used CP-SAT to enumerate the solutions. A heuristic for "interesting" solutions is those which only admit one valid bishop placement. For example:

    ........
    Q..B..Q.
    ........
    ........
    .......Q
    ........
    ........
    ...Q....
Where the bishop lies at the intersection of three queens' horizontal attacks. With these queens, no other bishop placement works.

Re: Chess puzzle I found in my dad's old book

#19

Post by hatthew »

I solved it with this, a pleasingly symmetric solution. I was surprised that a solution exists with all the queens in a row.

    . . . . . . . .
    . . . . . . . Q
    . . B . . . . .
    . . . . . Q . .
    . . . . . . . .
    . . . Q . . . .
    . . . . . . . .
    . Q . . . . . .

Re: Chess puzzle I found in my dad's old book

#20

Post by maest »

> In other words, after arranging the five black pieces, it must be impossible to place the white king anywhere without it being in checkmate.

I think this is a bit ambiguous and, strictly speaking, wrong for the solution as given.

In particular, this asks for the king to be in check _mate_. Does this require all black pieces to defend each other? Otherwise, white king on the board would not be in checkmate if you place it next to a queen and can immediately capture.

From the solution, you can see it's not a checkmate requirement, just a check requirement.

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