During the course of the year 2000, two brothers Andrew and Brady set out to research the family tree and began by listing the dates of birth of all the family members born during the period covering January 1, 1900 to December 31, 1999 inclusively.
Each date was recorded as three pairs of digits, written in succession to form a positive six digit decimal integer with a zero preceding any single digit day, month or year. Andrew followed the dd-mm-yy format, while Brady followed the mm-dd-yy format. For example, May 7, 1998 would be written as 070598 and 050798 respectively by Andrew and Brady.
Comparing the two different integers representing Chloe’s birth date, they noticed that one of them was a perfect square, and the absolute difference between them was a nonzero perfect square. The same was true for their versions of the birth date of Chloe’s sister Denise, who is younger by between one and two years.
When was Chloe born? What was the birth date of Denise?
Note: Try to derive a non computer-assisted solution, although computer program/spreadsheet solutions are welcome.