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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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..
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. |
