Question 227184: Ann, Barb and Cathy are all younger than 100. The sum of any two of their ages is the reverse of the digits of the remaining person's age. What are their ages?
I was doing o.k. until I hit the reverse digits line:(
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Ann, Barb and Cathy are all younger than 100.
The sum of any two of their ages is the reverse of the digits of the remaining person's age. What are their ages?
:
We know one thing about the reversal of digits, the difference between the two numbers is always a multiple of nine.
So all three ages have to be multiples of nine.
:
This narrows our choice of numbers to:18,27,36,45,54,63,81.
The sums of any two will be a multiple of 9 also
:
After a couple false hopes, I chose A=18; B=45
18 + 45 = 63, reversing that: C=36
and B + C
45 + 36 = 81, reversing that: A=18
and A + C
18 + 36 = 54, reversing this: B=45
:
Ann is 18
Barb is 45
Cathy is 36
:
As far as writing an equation to solve this, it would be extremely complicated, not practical, at least that's my opinion which is probably is not worth much.
Anyway, to date, no one has ventured to solve this one Carl
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