SOLITAIRE. 



737 



a straight line, 9-16-23. By the "equivalents" you can always succeed 

 in solving 1 the problem desired. 



We will now point out four transformations which are very easy to 

 effect, and result from the rule of " equivalents." 



1. Replacement of the two balls, situated on the same line and 

 separated by an empty cup, by one put into that cup. Thus I can replace 

 23 and 25 by a single ball at 24. 



2. Suppression of tierces. And by the above movement I suppress 

 the tierce 9-16-23. 



3. Correspondent "cases" are two holes situated in the same line 

 and separated by two cups. If two corresponding cups are filled, I can 

 suppress the balls which occupy them. So I can put aside 4 and 23 



Fig. 868. Correspondents and equivalents. 



4. It is permissible to move a ball into one of the correspondent cups if 

 it be vacant; thus I can put 10 into 29. 



These are the four transformations which can be made evident with 

 the rings, without displacing the balls. To do this we need have only seven 

 rings large enough to pass over the balls and to surround the holes in which 

 they rest. Let us take an example. 



Solitaire with 33 holes (fig. 869). Final solution of the single ball. 



1st Vertical row: 7 and 21 are occupied, and the intermediate hole 

 14, being empty, I place a ring upon 14. 



2nd Vertical row : No. 8 takes 1 5, and comes into 22 ; I place a ring 

 on 22. 



3rd Vertical row : I suppress the corresponding balls, 4-23 and 16-31, 

 there now only remains 9, so I place a ring on 9. 



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