Ego City's West Lake falls with swans, one lake one pair two swans more, one lake three three less, how many in total have fallen?
(Explanation: Huizhou is nicknamed "Ego City", and the West Lake in the city is a famous scenic area, consisting of 5 lakes: Feng, E, Ping, Ling, and Nan. The question means: one lake has one pair of swans with two swans more, one lake has three swans with three swans less, how many swans have fallen in total?)
19. Answer: 12 swans

Analysis:

Method one: (Arithmetic method) From "a pair of swans more than a lake", we know the number of swans is a multiple of 2; from "three swans less than a lake", we know the number of swans is a multiple of 3. Since $(2,3)=1$, we know the number of swans is a multiple of 6: $6, 12, 18, 24, \cdots$ Verification yields: a total of 12 swans landed.

Method two: (Algebraic method) Let the number of swans be $\mathrm{x}$, and they land in $\mathrm{Y}$ lakes. Then $2 \mathrm{y}+2=3 y-3$,

Solving for $y$ gives $y=5$, then $x=2 y+2=2 \times 5+2=12$, i.e., a total of 12 swans landed.