user703: I am looking into a website with starting positions for chess960.
000 BBQNNRKR
001 BQNBNRKR
002 BQNNRBKR
003 BQNNRKRB
004 QBBNNRKR
005 QNBBNRKR
...
959 RKRNNQBB

So there is a table that converts any number from 0 to 959 to a starting position. For example chess960(518) = 'RNBQKBNR' normal starting chess position.
What is this formula? How can I do this without storing all the table?

user888: From Wikipedia:

White's Chess960 starting array can be derived from its number N (0
  ... 959) as follows:
a) Divide N by 4, yielding quotient N2 and remainder B1. Place a
  Bishop upon the bright square corresponding to B1 (0=b, 1=d, 2=f,
  3=h).
b) Divide N2 by 4 again, yielding quotient N3 and remainder B2. Place
  a second Bishop upon the dark square corresponding to B2 (0=a, 1=c,
  2=e, 3=g).
c) Divide N3 by 6, yielding quotient N4 and remainder Q. Place the
  Queen according to Q, where 0 is the first free square starting from
  a, 1 is the second, etc.
d) N4 will be a single digit, 0 ... 9. Place the Knights according to
  its value by consulting the following table:
0     N   N   -   -   -
1     N   -   N   -   -
2     N   -   -   N   -
3     N   -   -   -   N
4     -   N   N   -   -
5     -   N   -   N   -
6     -   N   -   -   N
7     -   -   N   N   -
8     -   -   N   -   N
9     -   -   -   N   N

e) There are three blank squares remaining; place a Rook in each of
  the outer two and the King in the middle one.


703: <p>I am looking into a <a href="http://www.mark-weeks.com/cfaa/chess960/c960strt.htm" rel="noreferrer">website</a> with starting positions for chess960.</p>

<pre><code>000 BBQNNRKR
001 BQNBNRKR
002 BQNNRBKR
003 BQNNRKRB
004 QBBNNRKR
005 QNBBNRKR
...
959 RKRNNQBB
</code></pre>

<p>So there is a table that converts any number from 0 to 959 to a starting position. For example <code>chess960(518) = 'RNBQKBNR'</code> normal starting chess position.</p>

<p>What is this formula? How can I do this without storing all the table?</p>
 888: <p>From <a href="http://en.wikipedia.org/wiki/Chess960_numbering_scheme#Direct_derivation">Wikipedia</a>:</p>

<blockquote>
  <p>White's Chess960 starting array can be derived from its number N (0
  ... 959) as follows:</p>
  
  <p>a) Divide N by 4, yielding quotient N2 and remainder B1. Place a
  Bishop upon the bright square corresponding to B1 (0=b, 1=d, 2=f,
  3=h).</p>
  
  <p>b) Divide N2 by 4 again, yielding quotient N3 and remainder B2. Place
  a second Bishop upon the dark square corresponding to B2 (0=a, 1=c,
  2=e, 3=g).</p>
  
  <p>c) Divide N3 by 6, yielding quotient N4 and remainder Q. Place the
  Queen according to Q, where 0 is the first free square starting from
  a, 1 is the second, etc.</p>
  
  <p>d) N4 will be a single digit, 0 ... 9. Place the Knights according to
  its value by consulting the following table:</p>

<pre><code>0     N   N   -   -   -
1     N   -   N   -   -
2     N   -   -   N   -
3     N   -   -   -   N
4     -   N   N   -   -
5     -   N   -   N   -
6     -   N   -   -   N
7     -   -   N   N   -
8     -   -   N   -   N
9     -   -   -   N   N
</code></pre>
  
  <p>e) There are three blank squares remaining; place a Rook in each of
  the outer two and the King in the middle one.</p>
</blockquote>
