Enigmatic Code

Programming Enigma Puzzles

Enigma 1668: Square dates

From New Scientist #2834, 15th October 2011 [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?



One response to “Enigma 1668: Square dates

  1. Jim Randell 2 December 2011 at 5:36 pm

    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)
            prev = None

    Solution: The two dates are 01.10.25 and 02.10.25.

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