12. As shown in the figure, the large circle is a 400-meter track, and the track from $A$ to $B$ is 200 meters long, with a straight-line distance of 50 meters. A father and son start running counterclockwise from point $A$ along the track for exercise. The son runs the large circle, while the father runs straight each time he reaches point $B$. The father takes 20 seconds to run 100 meters, and the son takes 19 seconds to run 100 meters. If they run at these speeds, in which lap will the son first meet his father again?
The son meets his father for the first time while running the 3rd lap.
12.【Solution】First, we need to note: The father and son can only meet on the track segment from $\mathrm{A}$ to $\mathrm{B}$ in a counterclockwise direction, and the son runs faster than the father, so when they meet, the son must catch up to the father from behind.

The time it takes for the son to run one lap is $19 \times(400 \div 100)=76$ (seconds), which means the son reaches point $\mathrm{A}$ every 76 seconds. Similarly, the father reaches point $\mathrm{A}$ every 50 seconds. On the segment from $\mathrm{A}$ to $\mathrm{B}$ in a counterclockwise direction, the son takes $19 \times(200 \div 100)=38$ (seconds), and the father takes $20 \times(200+100)=40$ (seconds). Therefore, as long as the son reaches point $\mathrm{A}$ within 2 seconds after the father reaches point $\mathrm{A}$, the son can catch up to the father from behind. Thus, we need to find a multiple of 76 (this multiple represents the number of laps the son has completed when they meet) that is greater than a multiple of 50 but at most 2 seconds greater. That is, we need to find a multiple of 76 that, when divided by 50, leaves a remainder between 0 and 2. We can try this: $76 \div 50$ leaves a remainder of $26, 76 \times 2 \div 50$ leaves a remainder of 2. This fits our requirement. (In general, we should first observe the pattern of the remainders when multiples of 76 are divided by 50)

Therefore, when the father and son meet for the first time, the son has completed 2 laps, which means he is running the 3rd lap. Answer: The son meets his father for the first time while running the 3rd lap.