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 15, 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.
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 14, 22, 9, 17, 18, 26, and 20 which are indicated on the diagram by the line drawn through each vertically. They are all comprised in the three horizontal rows, 3, 4, 5.