English

## Did you know?

### Contest: the 9 queens problem

A predecessor: the 8 queens problem

A famous problem in chess is to arrange 8 Queens in 8*8 chess board, which is known to be 8 queens problem. Here, in this 8 Queens problem an individual should arrange 8 Queens in chess board without the interaction of other Queens. Each Queen should not meet other queens. The following board shows the output for 8 Queens problem,

This Eight Queens problem is famous all along and also it has its own history. This problem has been included in education.

To celebrate these nine years of chess variant webpages, they conducted a small contest: to look for the best solution to The 9 Queens Problem.

One queen more

The 9 queens problem, placing 9 queens without interaction in 8*8 chess board is impossible, so the team allowed to use pawns to add on the board to solve the puzzle. Now the solutions were too many. Finally the team announced to use less pawns to solve the puzzle and win the contest.

Roberto Lavieri has proved 10 Queens with 2 pawns. His solution follows, Place the QUEENS: a8, b5, c3, d1, d6, e4, f2, f7, g5, h3 PAWNS: d5, f3. He said a big no to find the solution for 9 Queens problem in 8*8 chess board with one pawn. With two Pawns he constructed this solution: QUEENS in a1, b3, c5, d3, d8, e6, f4, g2, h5. PAWNS in c3, b5 and also he mentioned as he don't have a proof for this solution.

More possibilities are there in n Queens problems with n*n chessboard.

Number of Total Solutions to the Queen's Problem:

 Board Total Solutions Unique Solutions 1 x 1 1 1 2 x 2 0 0 3 x 3 0 0 4 x 4 2 1 5 x 5 10 2 6 x 6 4 1 7 x 7 40 6 8 x 8 92 12 9 x 9 352 46 10 x 10 724 92 11 x 11 2,680 341 12 x 12 14,200 1,787 13 x 13 73,712 9,233 14 x 14 365,596 45,752 15 x 15 2,279,184 285,053 16 x 16 14,772,512 1,846,955 17 x 17 95,815,104 11,977,939 18 x 18 666,090,624 83,263,591 19 x 19 4,968,057,848 621,012,754 20 x 20 39,029,188,884 4,878,666,808 21 x 21 314,666,222,712 39,333,324,973 22 x 22 2,691,008,701,644 336,376,244,042 23 x 23 24,233,937,684,440 3,029,242,658,210 24 x 24 227,514,171,973,736 28,439,272,956,934 25 x 25 2,207,893,435,808,350 275,986,683,743,434 26 x 26 22,317,699,616,364,000 2,789,712,466,510,280

#### Latest Facts

##### Paradox of even and natural numbers

We would often think that there are more number of natural numbers than the even numbers because nat...

##### Math madness 0 by 0 equals to 1 by 2

If this is proved to be correct, everything we have learned in our life so far in Mathematics will g...

##### Benfords law (first-digit law)

This will be one of the world most unexplained phenomena you would ever see. The miracle of numbers ...

#### Related Facts

##### Microwave oven by percy spencer

Percy Spencer, an American Engineer accidentally discovered Microwave Oven while working on Raytheon...

##### Maximum possible chess moves is 10921506 possible position after 7 moves

The number of possibility chess moves after the white move's is 20 (ie 4 knight moves and 16 moves o...

##### John nash - a beautiful mind

A Beautiful Mind is the movie based on the life of john nash, who is said to be Nobel Laureate in e...

##### Time dilation: your twin sibling will get more youthful than you

Your twin sibling will get more youthful than you when he returns from the space travel. If your twi...

##### Grigori yakovlevich perelman a mathematician to solve most difficult problems in topology

Grigori Yakovlevich Perelman is a Russian mathematician, who made a history in Riemannian geometry a...

Daily Maths Topic Today - contest: the 9 queens problem.