The Deceptive Mathematical Puzzle: The Mother, Child, and Father

One intriguing question that has the power to both challenge and entertain the mind is the classic story involving a mother who is 21 years older than her child. In 6 years, the child will be 5 times younger than the mother. The question, however, is often asked: where is the father? Let's dive into the mathematical mystery and unravel the unexpected answer.

Mathematical Approach to the Problem

Let's define the variables:

Let the child's current age be (b). The mother's current age is (a b 21).

In 6 years, the child's age will be (b 6), and the mother's age will be (a 6 b 27).

According to the problem, in 6 years the child will be 5 times younger than the mother. This can be written as:

((b 27) 5 times (b 6))

Simplifying this, we get:

[(b 27) 5b 30]

Bringing all (b) terms to one side and constants to the other, we get:

[(b 27) - 5b 30]

[-4b 27 30]

[-4b 3]

[b -frac{3}{4}]

Since age cannot be negative, let's consider the negative value in the context of measurements. (-frac{3}{4}) years is equivalent to (-0.75) years or 9 months before the child's birth.

Interpreting the Result

With the son's age being (-0.75) years, we can calculate the mother's age:

[a b 21 -frac{3}{4} 21 frac{-3 84}{4} frac{81}{4} 20.25] years.

In 6 years, the mother will be (20.25 6 26.25) years old, and the child will be ( -0.75 6 5.25) years old, or 5 years and 3 months. At this point, the mother will be 5 times older than the child.

The puzzle's final twist is about the father. Since the child's age is negative (meaning the child is yet to be born), the father is involved in the creation of the child, either through pregnancy or recently having conceived the child.

Conclusion

The riddle is not just a mathematical puzzle but a clever tale of life's beginnings. The father, in a sense, is the one laying the groundwork for the birth of the child. Thus, the answer to the question is that the father is involved in the actual process of conception or creation—perhaps in the very act of procreation itself.