∵2450=2×5×7×5×7,

I like the following nine situations: 50, 7, 7; 49, 10,5; 7, 10,35; 7, 14,25; 5,7,70; 2,35,35; 2,25,49; 5,7,70; 5,5,98,

And teacher B knows his age, so the probability of being twice as big as teacher B is only 5,10,49 and 7,7,50.

And since Teacher A said that the missing condition is that all three people are younger than him,

Then a is older than 49 years old;

If a is over 50,

Then even if all three people are younger than A, Teacher B can't judge their ages.

To sum up, A can only be 50 years old, so B's age is (49+ 10+5)÷2=32 (years old).

The three neighbors are 49 years old, 10 years old and 5 years old.

This question examines simple reasoning problems and thinks about how to solve them in combination with the meaning of the question;

Given that the age product of three neighbors is 2450, all possible situations can be obtained according to 2450=2×5×7×5×7, and Teacher B knows his own age, then the combination with half the sum of the ages in the combination is possible.

Then, according to the fact that all three neighbors are younger than Teacher A, combined with the above conclusions, we can deduce the ages of Teacher A, Teacher B and the three neighbors respectively, and solve them accordingly.