After all solutions have been processed, the table is sorted in ascending or descending sequence to determine the number-piece configurations with the least or most occurrences. The results of the analysis suggest some challenging new problems presented in the following sections. Configurations with the Most Solvable Problems When solutions with insignificant number pieces are included, there are several number-piece configurations where piece X can be placed in any vacant square except the center and all of the resulting problems are solvable. These are the only analyzed problems groups, for either board, with number-piece configurations where all problems are solvable. Remember that letter pieces never begin in the center.
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Configuration 1 in figure 3, from problem group 1-4, has 16 solvable problems where all number pieces are significant. This is the most of any analyzed problem group for the 5 x 5 board. Configurations 2 and 3 in figure 3, from problem group 1-5, each have 15 solvable problems where all number pieces are significant. The other 4 problems for each configuration are solvable, but have insignificant number pieces. Configuration 4 in figure 3, from problem group 1-6, has 13 solvable problems where all number pieces are significant.