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 Subj:.....My Grandfather's and My Age (S677)           From: MathNexus.wwu.edu           on 1/6/2010 Drawing from MathNexus...

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Source: http://mathnexus.wwu.edu/Archive/problem/detail.asp?ID=184

In 1932, my dad was as old as the last two digits of his
birth year.  When he mentioned this interesting coincidence
to his grandfather, my dad was surprised when his grandfather
said the same thing was true for him as well.  Believe me,
it's quite possible and I am able to prove it too.  How old
was my father and his grandfather in 1932?

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 Drawing from tom on 8/21/2009
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Note: Is there anything special about the year 1932?  That
is, could the problem still be solvable for years other than 1932?

Source: Yakov Perelman, Mathematics Can Be Fun, Moscow: MIR Publishers, 1985

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 Finger pointing down from darrell94590 on 1/2/2006
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 Drawing from Ripleys-Believe It Or No
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THE SOLUTION

Solution Commentary: After some playing, you should
discover that everything can be summarized by two "key"
equations:
2(10a+b) = 32 and 2(10c+d) = 132
where my father was born in 19ab and his grandfather in
18cd.  The solution quickly follows from this...

Now, as to the year 1932...what happens if you shift to
1934...1960...1998?  And, why am I forcing the year to
end in an even digit?  Could this ever happen in the 21st
century?
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 Drawing from tom on 8/21/2009
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Solution:

In 1932, if my dad were born in 1916, he would be 16 years old,
and if his grandfather were born in 1866, he would be 66.
In 1934, if my dad were born in 1917, he would be 17 years old,
and if his grandfather were born in 1867, he would be 67.
In 1960, if my dad were born in 1930, he would be 30 years old,
and if his grandfather were born in 1880, he would be 80.
In 1998, if my dad were born in 1949, he would be 49 years old,
and if his grandfather were born in 1899, he would be 99.
Since you have to divide by two in both of the above equations,
this only works on even years.  If we go into the 21st
century either my dad's age will be very young, or his
grandfather will be very old, or both.

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