by omitting the "Q", giving -N-N- for the standard SP, so its N5N code is 5. In general idn = (bishop's code) + 16* (queen's position) + 96* (N5N code) For the standard SP, idn = 6 + 16*2 + 96*5 = 518 Going the other way, starting with an idn, divide it by 16 and get idn = q1*16 + r1. r1 gives the bishop's code, so put the bishops on the board. Then divide q1 by 6. q1 = q2*6 + r2. r2 gives the queen's position, so put it on the board. q2 gives the N5N code, so put the knights on the board (of course skipping over the bishops and queen). Starting with idn = 518, we get 518 = 32*16 + 6, and 32 = 5*6 + 2 so the bishop's code is 6, the queen's position is 2 and the N5N code is 5 with configuration -N-N-. If asterisks denote blank squares, the first rank fills up as: **B**B** **BQ*B** *NBQ*BN* All of the multiplication and division can be eliminated by using the NQ-skeleton table below. It contains all of the 60 possible NQ-skeletons, and directly refers to all of the SPs with bishop's code 0, i.e. with bishops on a1 and b1. Given an SP, extract the bishop's code, the NQ-skeleton and its N5N configuration. The six skeletons in each of the 10 blocks in the table all have the same N5N configuration, and the blocks are arranged according to the N5N table above. It is easy, then, to find the appropriate block, and look inside for the entry with the "Q" in the desired place, say at No. M. Then idn = (bishop's code) + M. For the standard SP, we extract 6 -NQ-N- and -N-N-. The desired block is the middle one in the second row, and the desired skeleton is at No. 512. We get idn = 6 + 512 = 518. Going the other way, given an idn, locate, in the table, the largest number, say M, that is less than or equal to idn. Then idn - M gives the bishop's code, and the skeleton at M shows how to fill in the rest of the pieces. Given idn = 518 we locate 512, with NQ-skeleton -NQ-N-, in the table, and get bishops code = 518 - 512 = 6. Preliminaries Both methods take account of the positions