Direct Derivation
White's Chess960 starting array can be derived from its number as follows:
a) Divide the number by 960, determine the remainder (0 ... 959) and use that number thereafter. Position number 960 is identical to position number 0.
b) Divide the number by 4, determine the remainder (0 ... 3) and correspondingly place a Bishop upon the matching bright square (b, d, f, h).
c) Divide the number by 4, determine the remainder (0 ... 3) and correspondingly place a Bishop upon the matching dark square (a, c, e, g).
d) Divide the number by 6, determine the remainder (0 ... 5) and correspondingly place the Queen upon the matching of the six free squares.
e) Now only one digit (0 ... 9) is left on hand; place the both Knights upon the remaining five free squares according to following scheme:
| Digit | Knight positioning | ||||
| 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 |
f) The now still remaining three free squares will be filled in the following sequence: Rook, King, Rook.
Read more about this topic: Chess960 Numbering Scheme
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