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Programming Enigma Puzzles
From New Scientist #2014, 27th January 1996 [link]
I have a lucky number. When the numbers of a date add up to the square of my lucky number I call that a “lucky day”. (For example, if my lucky number were 11 then 24/3/94 would be a lucky day since 24 + 3 + 94 = 121). I especially like the lucky days which fall on Sundays.
I once noted the occurrences of my lucky days as they happened over a period of three consecutive calendar years. I had one day each month. Furthermore, there were more lucky Sundays in the first year than in the second, and more lucky Sundays in the second than the third.
What was the date of the first lucky day in that three-year period?