1880.1 50, J [Frazer. 



Second Method. 



Number one heads the outside column. 

 Solutions only possible when 12 and 14 of the middle numbers are diag- 

 onally adjacent. Bring the 11 alongside of the 12. 



I. The middle numbers occur as some combination of Table I. 



1. The increase of outside numbers with motion of watch bands ; a 3, 



and c 1. 



2. Increase of outside numbers against motion of watch hands ; d 1, 



and b 2. 



II. The middle numbers some combination of Table IT. 



1. Increase of outside numbers with motion of watch hands; b 3, 



and d 1. 



2. Increase of outside numbers against motion of watch hands ; c 2, 



and a 1. 

 Number fifteen leads. Solutions only possible when 1 and 3 are diagon- 

 ally adjacent. 



Bring the 5 alongside the 4. 



III. The middle-numbers occur as some combination of Table III. 



1. Decrease of outside numbers with motion of watch hands ; b 2, 



and d 1. 



2. Decrease of outside numbers against motion of watch hands ; a 3, 



and c 3. 



IV. Middle numbers occur as some combination of Table IV. 



1. Decrease of outside numbers with motion of watch hands ; a 3, 



and c 1. 



2. Decrease of outside numbers against motion of watch hands ; b 2, 



and d 2. 



Third Method. 

 The numbers read from left to right on the first and third lines and from 

 right to left on the second and fourth, or vice versa, thus : 



12 3 4 



8 7 6 5 



9 10 11 12 

 15 14 13 



The order of outside numbers is 1. 2, 3, 4, 8, 7, 6, 5, 9, 10, 11. 



Solutions are only possible when 12 and 15 or 1 and 4 are diagonally ad- 

 jacent. The first four numbers pass 13-12 in I and II, and 3-4 in III and 

 IV, in the order named, the head of the column coming to rest at the 

 square diagonally adjacent to the 12 or the 4 respectively. 



Number one heads the column. The upper line is full. 

 I. The middle numbers a combination of Table II. 



1. First four numbers increase with motion of watch hands ; a 2, and 



d2. 



2. First four numbers increase against motion of watch hands ; b 1, 



and c 3. 



