place both bishops at the first base row, then the six pieces in the sequence of the found row of the King's Table upon the six free places left over. Finally the black pieces will be placed symmetrically to White's base row. Consider the SP-518 arrangement. The largest multiple of 16 less than 518 is 512, so we search for 512 in the King's table and the remainder, 6, in the Bishop's table. In the King's table, number 512 is "RNQKNR". In the Bishop's table, "--B--B--" is at number 6. We insert the pieces from the King's table into these gaps to get the starting array "RNBQKBNR", which is the starting order in traditional chess. Scharnagl's methods For years, Reinhard Scharnagl has championed the desirability of giving each of the starting positions (SP) a unique identification number (idn) in the range 0-959 or, perhaps, 1-960. He has presented his methods on the internet and in books. See the external references. As an application, a random number generator could make one probe into the range at hand for a random number, and produce a random SP. Late in 2005, the program Fritz9 became available. It has a Fischer random chess option, but, for some unexplained reason, it assigns idns to SPs in a different way. Rather than requiring a giant table with 960 entries, both methods can use some smaller tables and some arithmetic. The methods described below are appropriate for the idn range 0-959. For the idn range 1-960, he recommends conversion by dividing by 960 and working with the remainder. This has the effect of assigning to idn 0 the SP that was at idn 960, and leaving the other idn SP matchups unchanged. If this calculation is applied in the idn range 0-959, nothing is changed. For any SP, after skipping over the bishop's, the queen may occupy any one of six possible squares, and they are numbered from left to right (from White's perspective) 0,1,2,3,4,5. The two knights, then, can appear in any of the remaining five squares (skipping over bishops and queen) in 10 ways. These are shown and numbered in the N5N table. For any SP, both the queens position and the N5N configuration are immediately available from the NQ-skeleton. The queen's position is the number of characters to the left of the "Q", giving 2 for the standard SP. The N5N configuration is obtained