If Bill’s age in years is appended
to Alice’s age, the resultant four
digit integer is a perfect square.
The same thing will be true thirteen
years from now. What are Bill’s and
Alice’s ages?
A nice pencil and paper problem! Maybe only D2, definitely not warranting a computer program. Anyways lets start solving:
Call the two perfect squares M^2 and N^2. The 13 year difference means that M^2 + 1313 = N^2.
Rearrange into (N-M)*(N+M) = 13*101. Then working over integers N-M=13 and N+M=101.
Solving the system yields N=57 and M=44.
Then M^2=1936 and N^2=3249. Check 32-19=13 and 49-36=13, good!
So the answer is Bill’s and Alice’s ages now are 19 and 36.
Analytic Solution
