# Challenge suggestion for MAY - Domination CHESS problems !

• ### General discussion

• Domination CHESS problems !

Another kind of mathematical chess problems is a domination problem (or covering). In these problems it is requested to find a minimum number of pieces of the given kind and place them on a chess board in such a way, that all free squares of the board are attacked by at least one piece

So how minimum KNIGHTS is required or you have to put on a chess board for they all cover the 64 squares. ??

• Changed type Tuesday, April 19, 2016 9:47 PM
Monday, April 18, 2016 8:24 PM

### All replies

• This is my first step of this challenge: CNV255-0.

Click to move or remove a knight.

Nonki Takahashi

Sunday, May 1, 2016 10:31 AM
• great !! a really fun challenge for the mind !

I found a superb website about chess algorithms:

AI Chess Algorithms

The program implements the following concepts and algorithms:
1. Board Representation
2. Min-max Searching
3. Alpha-beta pruning
4. Null move heuristic
5. Quiescence searching
6. Static board evaluation functions
7. Optimizing board evaluation functions via genetic algorithms
8. Opening Move Database

Sunday, May 1, 2016 2:14 PM
• As the second step, I'm trying to find symmetric pattern like this.

There are 65536 patterns in this figure.  The pattern number is from 0 to 65535.

For example, Pattern 1 has 4 knights a1, h1, h8, and a8.  Pattern 3 (= 1 + 2) has 8 knights a1, b1, h1, h2, h8, g8, a8 and a7.

Nonki Takahashi

Sunday, May 29, 2016 4:49 AM
• My second program is still running.  But it already has two answers - pattern 78 and 3136.

Pattern 78 (=2+4+8+64) has 16 knights, and pattern 3136 (=64+1024+2048) has 12 knights.

Nonki Takahashi

Sunday, May 29, 2016 5:21 AM
• After running about 8 hours, I stopped the second program (CNV255-1).  Because pattern 49152 (=32768+16384) was the last pattern that has only two knights.

So, the minimum knights (in symmetric pattern 3136) is 12.

Nonki Takahashi

Sunday, May 29, 2016 9:57 AM
• Fantastic !!
Sunday, May 29, 2016 1:32 PM
• Just4fUn and chess, not about dominant knights but opening a new game. ID: DBG614
There's just to apply a single popular opening move for an h dive between tangerine and samba.
Wednesday, June 1, 2016 9:48 PM
• Cool !!! as i am a chess player, your program is great !!
Thursday, June 2, 2016 2:09 AM
• Great and who is the first sb chess Play?

Best Regards Martin

Thursday, June 2, 2016 5:38 AM