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Anything involving "th" would be useless, as various combinations, such as 1st, 8th or 25th, 1st, etc., would fulfill them many times over.
So we're restricted to "st", "nd" and "rd". Some combinations are impossible: "st st", "st nd", "st rd", "nd nd", "nd rd" and "rd rd". But three combinations are possible, all connecting the last Friday in February to the first Friday in March: "rd st" in a leap year, or "nd st" or "rd nd" in a non-leap year.
The example year given shows a Feb. 3, indicating the last Friday of February that year was Feb. 24, 2006. During the time period in question, every year divisible by 4 was a leap year. From a non-leap year to the following year, the date of the last Friday goes up by 6 or down by 1, depending on whether or not that year can contain the +6 date. From a leap year to the following year, the date goes up by 5 or down by 2 depending on whether or not the +5 date exceeds 28 (as the year after a leap year is always a non-leap year).
The first scrap Susan found, "rd nd", indicates a non-leap year in which Feb. 23rd was the last Friday of the month, followed by March 2nd as the first of the following month. Counting backward in the calendar, keeping track from 2006, you can see this happened in 1951, 1962, 1973, 1979, 1990, 2001 and 2007. You could also look at a calendar for 1950 and count forward to find the same thing. Susan knew what box (decade) she was in but still didn't know the date from this clue, so it could be either the 1970's or the 2000's, each of which had two such occasions, except that she had opened "one of the earlier boxes", so it must have been "the seventies" (she knew that all along from the label; we only just now figured that out).
In the 1970's the only unique scrap of the type under discussion would have been "nd st", representing Feb. 22nd and March 1st, 1974. There were no other non-leap (or leap for that matter) years in that decade with Feb. 22 on a Friday.
From Enigma No. 1453, by Susan Denham, New Scientist, 28 July 2007. |
