A date can be written as DD/MM/YY, so that for example 01/08/16 means 1 August 1916. But if you concatenate just the digits, 010816 happens to be a perfect square, as it is 104². Call such a day a "square day".

Adrian's grandfather was one of six cousins born on different square days in the same year, which was a leap year in the 20^th century. All of them died on square days in leap years, and none of them lived to see age 99. Each of them except Adrian's grandfather died in the same month as his or her birthday.

What was Adrian's grandfather's date of birth?

Adrian's grandfather was born [548²] 30 MAR 1904 and died on one of the following dates, with his possible age at death parenthisized following the given date:
[246²] 06 MAY 1916 (12)
[104²] 01 AUG 1916 (12)
[332²] 11 FEB 1924 (20)
[318²] 10 NOV 1924 (20)
[144²] 02 JUL 1936 (32)
[106²] 01 DEC 1936 (32)
[388²] 15 MAY 1944 (40)
[362²] 13 OCT 1944 (40)
[284²] 08 JUN 1956 (52)
[266²] 07 JUL 1956 (52)
[142²] 02 JAN 1964 (59)
[224²] 05 JAN 1976 (71)
[174²] 03 FEB 1976 (71)
[176²] 03 SEP 1976 (72)
[226²] 05 OCT 1976 (72)
[490²] 24 JAN 2000 (95)
[510²] 26 JAN 2000 (95)
[480²] 23 APR 2000 (96)
[520²] 27 APR 2000 (96)
[470²] 22 SEP 2000 (96)
[530²] 28 SEP 2000 (96)

Of Adrian's grandfather's cousins, we know the following:
The 1st to die, at age 11, was the cousin
     born [202²] 04 AUG 1904
     died [104²] 01 AUG 1916
The 2nd to die, at age 19, was the cousin
    born [348²] 12 NOV 1904
    died [318²] 10 NOV 1924
The 3rd to die, at age 31 or 51, was the cousin
    born [448²] 20 JUL 1904
    died [144²] 02 JUL 1936 or [266²] 07 JUL 1956
The 4th to die, at age 96, was the cousin
    born [102²] 01 APR 1904
    died [480²] 23 APR 2000 or [520²] 27 APR 2000

Edited on November 30, 2007, 2:19 am

Posted by Dej Mar on 2007-11-29 11:27:46