The Fourteen Total Switches
A number of challenging questions relating to the limits of improving one side's prospects by individual interchanges of cards have been posed, and in some cases answered, by Ken Lebensold. He provides this intriguing subset of the type:
A deal and contract pair is said to satisfy "the total switch condition" if, double-dummy, South, as declarer, cannot make the contract in the layout of the deal but could succeed if any of North's cards were interchanged with a higher card in the same suit held by any of the other three players. The 14 sub-mysteries of Mystery # 6 are: For each of the 14 contracts one notrump through seven notrump and one spade through seven spades, find a deal satisfying the total switch condition in which the sum of the ranks of North's lowest cards in the four suits (void = 0, ace = 1, king = 2, . . . , three = 12, deuce = 13) is as high as possible. [Note that there might be more than one pattern leading to the highest possible total. For example, North's lowest cards might be 3-3-3-3 or 4-4-2-2, each with a rank total of 48.]
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