x y z = 12236

X+y+z = 70, and the professor's age is 35. According to the professor's age, he is at least 7 years older than the oldest one, we can know that the maximum Z will not exceed 28, so X+y is at least 42.

So at least one of x and y should be greater than 2 1. )

Z must be the biggest. So z can only be one of 28, 27, 26, 25, 24, 23, 22.

Age must be an integer, so the product of x and y is also an integer. In other words, 12236 must be divisible by z, so 27, 26, 25, 24, 22 are excluded. Therefore, z= 28 or 23. x y = 12236/28 =437。 Or 12.

But if x y = 532, then x and y are at least (532 under the root sign) = 23.7. This does not meet the requirement that z is the maximum number, so it is discarded.

The mantissa of 437 is 7, which can only be 1×7 or 3×9. According to x+y = 42, it is easy to get that one of x and y is 23 and the other is 19.

So the answers are x = 23, y = 19 and z = 28.

The process of solving the problem is as above.