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 Q and A (Posted on 2022-03-06)
Q(posed by a high-school student to his math teacher):
Could you tell my age after I disclose the fact that the current number of years of my existence equals the sum of digits representing my age plus their product?
A(provided after 2 minutes of pondering upon the subject): Yes, I have figured out your age, but I must tell you that if the question was posed by phone by a stranger whom I do not see I would not be able to solve this problem.

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 Solution | Comment 1 of 2
Let the student's age be a 2 digit number xy (concatenated).  For now, allow zero as a possible value for x to account for single digit ages.
The student's statement is represented by:
(10x + y) = x + y + x*y
9x = x*y
9 = y   (oops, did I just divide by zero?)
So far, the age can be any 2 digit number ending in 9.  Even 09 satisfies this mathematically.  But if the student's age is the single digit 9, then the statement becomes:
9 = 9 + 9 which fails.   (I guess I shouldn't have divided by zero)
So the possible ages are {19, 29, 39, etc}
Since it is given that the student is in high school,
the only possible answer is 19.

Edited on March 6, 2022, 7:16 am
 Posted by Larry on 2022-03-06 07:13:40

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