May 2016

<<April May June>>

Ponder This Challenge:

Find two different ways to place chess pieces on an 8x8 board so that each square is threatened exactly the same number of times.

Note that we are using single color pieces and you can use as many pieces as you want (not limited to the standard chess set); but each square can hold at most one piece.

Supply your answer as two sets of 64 characters (k for king, q for queen, r for rook, b for bishop, n for knight; p for pawn, and = for empty square).

For example, on a 4x4 board, placing 4 queens as follows:

= q q =

= = = =

= = = =

= q q =

gives the following threats numbers:

2 2 2 2

2 3 3 2

2 3 3 2

2 2 2 2

There is another way to get to the same numerical solution as well.



Note that a chess piece does *not* threaten the square it is occupying (otherwise the problem would be too simple).

Update (02/05):

Find two different ways to place chess pieces on an 8x8 board so that each square is threatened exactly the same number of times, such that no piece is placed in the same position in both the boards, like the pair =qq= ==== ==== =qq= and ==== q==q q==q ==== in the 4x4 case; not a pattern that creates the same attack number for all the squares (like the trivial empty board). Unlike real chess, the pieces are ignoring others in their way: attacking through them as in the 4x4 example.

Update (03/05):

To earn a '*', find a solution without using pawns; to get '**' find a solution using all other five pieces types (k,q,r,n,b).

We will post the names of those who submit a correct, original solution! If you don't want your name posted then please include such a statement in your submission!

We invite visitors to our website to submit an elegant solution. Send your submission to the ponder@il.ibm.com.

If you have any problems you think we might enjoy, please send them in. All replies should be sent to: ponder@il.ibm.com