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The numbers that are squares and can represent dates in any century and could be leap years (they're divisible by 4) are the following:
240100
260100
230400
270400
220900
280900
300304
10404
200704
40804
121104
91204
60516
10816
110224
101124
20736
11236
150544
131044
80656
70756
20164
50176
30276
30976
51076
Regardless of how you count centuries, both 1900 and 2000 are ineligible for the grandfather's year of birth, as 1900 was not a leap year and 2000 is too recent for a grandfather to have been born.
Of the year-ending two digits remaining, only '04 has six separate dates for the six separate cousins. As 2004 is too late for a grandfather to have been born, it must have been 1904.
March (i.e., month 03) is unique to that year (within the 99 years beginning then), while the other months' specified for that year recur in later 20th century years: April in 2000, July in 1956, August in 1916 (that cousin was almost 12 when he/she died, but he/she didn't need to be a grandfather), November in 1924 and December in 1936.
So Adrian's grandfather was born 30 March 1904.
From Enigma No. 1464 by Adrian Somerfield, New Scientist, 13 October 2007.
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