## Puzzle #5 (Answer): Leaping to Conclusions

Puzzle #5: A Royal Mystery posed the following question:

Gregory was born on a Monday in New York City.  His father sent out Western Union telegrams to announce the birth.  The family later moved to London.  On his seventh birthday, which was also a Monday, the boy saw the British monarch.

Was the monarch a king, or a queen?

The key to the puzzle is that Gregory’s seventh birthday is the same day of the week as the day he was born.   Every new birthday advances the day of the week by one, or by two if there is an intervening leap day.   The only way for Gregory to cycle back to a Monday on his seventh birthday would be for him to have never seen a February 29.

The boy’s name suggests our Gregorian calendar system. Under the reforms of Pope Gregory XIII, every fourth year is a leap year, except for multiples of 100 that are not also multiples of 400.  So 1900 was not a leap year, 2000 was a leap year, and 2100 will not be a leap year.

The mention of the Western Union telegram limits Gregory’s birth to the period from the mid-1800s to 2006, when the telegram service ended.  So his first seven years must have included the year 1900.  He must have been born after February 29, 1896 and must have turned seven before February 29, 1904.  His seventh birthday fell somewhere in the range of March 1, 1903 to February 28, 1904.  Edward VII was the King of England at that time.

The puzzle was solved on this blog after two weeks.  I also posted it on the Brainteasers Forum at Wilmott.com, where a solution popped up thirteen minutes later (it’s not easy to tease those brains).

The puzzle’s relevance to financial modeling is that accurate financial calculations require accurate time measurements.  Unfortunately, popular software packages do not always measure time correctly.

Excel represents dates by serial numbers, starting with 1 for January 1, 1900, 2 for January 2, 1900, and so on (the count runs from 1904 on the Mac version of Excel). Today, February 29, 2012, should have serial number 40,967, but Excel counts it as 40,968. Why? Because Excel counts February 29, 1900 as a real date, even though 1900 was not a leap year.  Microsoft deliberately copied the mistake from Lotus 1-2-3 so that Excel would be compatible with the older software.

Excel has an intentional Y1.9K bug, but it probably won’t cause you any trouble.  Fortunately, Excel handles the year 2100 correctly (it won’t be a leap year), so there is no Y2.1K bug to worry about.

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