All Questions
Tagged with checkerboard no-computers
6 questions
6
votes
2
answers
449
views
Pawns and a chessboard with no three aligned
This little problem crossed my mind and appeared to be not quite trivial.
How can you place P pawns on a chessboard with the constraint that no pawn is exactly midway between two other pawns?
Sure ...
- 31.4k
3
votes
1
answer
438
views
Genies' chess on a 10×10 board
The work of Hearth Taxel revealed some other results related to genies' chess. For example, there is an arrangement $A$ of pawns on a 10×10 board such that no 3×3 submatrix is empty and
$A$ is ...
- 8,725
4
votes
1
answer
211
views
Chess - I will eat!
Suppose that you are playing White, and your aim is to eat a black piece (pawns qualitfy) in the fewest moves as possible and Black are not cooperating at all, and, even more, Black's aim is to ...
- 6,518
32
votes
5
answers
5k
views
How can 3 queens control the white squares?
It is well known that there is no way of arranging 4 queens on a checker board in such a way that every square is occupied or threatened.
Now consider a slight variation where we only need to cover ...
- 10.4k
18
votes
4
answers
2k
views
Paint 21 Squares of a 7×7 Board Without Forming a Rectangle
Got a nice puzzle from my friend, when he was competing in IWYMIC/IMC 2011.
Paint $21$ of the $49$ squares of a $7 \times 7$ board so that no four painted squares form the four corners of a rectangle....
- 34.4k
3
votes
1
answer
595
views
Row of alternating coin
I stumbled upon a mathematical puzzle that goes like this: You have 2n coins that alternate between head and tail. For example, if n=3, then it looks like H T H T H T, where H = head and T = tail. To ...
- 31