All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Numbers
Square Birthdays (Posted on 2007-11-29) Difficulty: 3 of 5
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 104. 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 20th 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?

  Submitted by Charlie    
Rating: 3.3333 (3 votes)
Solution: (Hide)
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.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
answerK Sengupta2008-02-06 06:11:49
re(3): Do April Fools live longer? (SPOILER)brianjn2007-11-30 03:37:41
re(2): Do April Fools live longer? (SPOILER)Dej Mar2007-11-30 02:21:54
re: Do April Fools live longer? (SPOILER)brianjn2007-11-30 00:49:23
re: Some Unanswered Questionsbrianjn2007-11-29 18:10:53
SolutionSome Unanswered Questionsbrianjn2007-11-29 17:34:36
SolutionDo April Fools live longer? (SPOILER)Dej Mar2007-11-29 11:27:46
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information