## Afi A

illl pli^lli 111

4. 122 moves considered. A classic example is the task of placing the eight pieces of one color so that the largest number of moves can be made. The proved maximum of 100 was achieved by M. Bezzel in 1848 (see page 62 of The Sixth Book of Mathematical Games from Scientific American). If all 16 men of one color are used, the maximum was believed for 10 years to be 119 moves until Nenad Petrovic increased it in 1949 to 122 [see Figure 116, No. 4], When I first saw this pattern, I was unable to count more than 104 moves until I realized that a promoted pawn must become one of four different pieces, each of course a different move. (Modern chess laws do not allow a pawn on the eighth rank to remain a pawn.) The record for the 16 black and white pieces is 173, for all 32 men it is 164, and for a legal position with no promoted men or promotion moves it is 181. The present record for an illegal position is shown in Figure 116, No. 5. By arranging the colors of the border queens as shown, W. A. Shinkman, in 1923, achieved 412 moves. Captures are, of course, counted as moves.

The minimum number of moves for the eight pieces of one color is 10 (see my The Unexpected Hanging and Other Mathematical Diversions, page 88). The same position also minimizes the number of pieces (three) among the eight that are able to move. Ten also is the record for minimum moves when the 16 pieces of both colors are used. In 1923 T. R. Dawson found the record minimum for all 32 men in a legal position [see Figure 116, No. 6]. Only two moves can be made. E. Fielder showed in 1938 how the same 32 men can be legally placed so

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