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We can just translate their statements into algebra:


Aunt Isabel received Reasoning After looking at the numbers Therefore the totals are, by child's age


If it weren't for leap years, the Gregorian calendar would repeat every 7 years. But due to the 4-year frequency of 29 Feb, it actually repeats every 28 years, except in some rare cases. So the task is to find one of those rare cases: a 7-year span without a leap year.


I wrote a little bit of code that attempts to work this out. It searches every date from an arbitrary point in time that gives the man a chance to be up to 130 years old, and checks to see if that date and the date seven years later are both Sundays. If this check is true, it returns the date as the date of birth and calculates the age. Paste this code into ...


There are a few tricksy ways to make this work (e.g. by bending semantics with a birthday on 29 February in Southern Hemisphere summertime, and claiming that 28 years later - when the Gregorian calendar usually repeats itself, with all dates falling on exactly the same days of the week - it's technically "only my seventh birthday", for instance...)....

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