Two mathematics teachers were talking at a New Year's Eve party in 2001. The retirement age for teachers was 60 years old, and both were still working. Being mathematicians they turned to discussing the date, and mathematical curiosities.
The first said that she had realised that in the past the year was the square of her father's age at that time. Sadly her father had passed away at the age of 100 (another square, but not relevant to this puzzle).
The second remarked that by coincidence she expected the year to be the square of her age before her 100th birthday.
In which years were the first teacher's father and the second teacher born?
The first thing to do is to find years either side of 2001 that are square numbers. 44 x 44 = 1936 and 45 x 45 = 2025, so these are good candidates.
If the father was 44 in 1936 he was born in 1892 and died in 1992, with the first teacher being born after 1942 to be under 60.
The second teacher was born in 1980, and will be 45 in 2025.
We can rule out other square years. 43 x 43 = 1849 and if the father was born in 1806, and so died in 1906, he would have been dead by the earliest birth year for his daughter. And if the second teacher was to be 46 in 2116 (46 x 46) then he would not yet be born.