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Programming Enigma Puzzles

20 June 2022

Posted by on **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?

[enigma859]

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This Python program runs in 81ms. (Internal run time is 17.9ms).

Run:[ @replit ]Solution:The first lucky day was 16th January 1983.The lucky number is 10, so we are looking for dates that sum to 100.

In 1983, 1984, 1985 we have:

Further back in time we can find more solutions (some with different lucky numbers):