Enigmatic Code
Programming Enigma Puzzles
Enigma 1668: Square dates
Posted by on 2 December 2011
From New Scientist #2834, 15th October 2011 [link] [link]
4 December 2009 is the most recent date that qualifies as a perfect square date when written as day, month, year with two digits for each element, that is as 04.12.09: 41209 is the square of 203.
Using the same format, what is the only instance in any century of two consecutive dates that are both perfect squares?
[enigma1668]
Enigmatic Code 
The following Python program runs in 91ms.
from enigma import is_square def fmt(dd, mm, yy): return '{dd:02d}.{mm:02d}.{yy:02d}'.format(dd=dd, mm=mm, yy=yy) prev = None for yy in range(100): for mm in range(1, 13): for dd in range(1, 32): n = dd * 10000 + mm * 100 + yy if is_square(n): if prev: print(fmt(*prev), fmt(dd, mm, yy)) prev = (dd, mm, yy) else: prev = NoneSolution: The two dates are 01.10.25 and 02.10.25.