733 



SCIENTIFIC RECREATIONS. 



4th Vertical row: I suppress the correspondents 10-29, put 2 into 17, 

 and I place a ring upon 17. 



5th Vertical row : I suppress correspondents 6-25, put 33 into 18, and 

 I place a ring upon 18. 



6th Vertical row: No. 12 takes 19 and comes to 26 ; I place a ring 

 on 26. 



7th Vertical row : No. 20 is the only ball ; I place a ring on 20. 



(It must be understood that these operations should be proceeded with 

 mentally ; the balls must not be disturbed.) 



We have thus reduced the problem to seven ringed balls, which are 1 4, 

 22, 9, 17, 1 8, 26, and 20 which are indicated on the diagram by the line 



\ 



o 



O 



o 



-e- 



o 



o 



o 



o 



o 



o 





Fig. 869. Single ball solution. 



drawn through each vertically. They are all comprised in the three hori- 

 zontal rows, 3, 4, 5. 



We can now set to work upon these three rows in the same manner as 

 before, considering the rings as balls. 



3rd row : We find (and leave) a ring upon 9. 



4th row : The two corresponding rings, 17-20, neutralize each other, 

 and we suppress them. We carry 14 to 17, and take 17 with 18, which 

 comes into 16. We leave a ring on 16. 



5th row : Carry the ring 26 to 23, take 23 with 22, which comes thus 

 to 24, and we leave a ring on 24. 



We now have reduced our problem to three rings, 9, 16, and 24, all in 

 the central square, indicated in the diagram by horizontal bars. It is easy 

 to see that 9 will take 16 and 24 and come into 25, and 25 will remain, 



