CRACKING THE CODE
Sam Townsend presents his monthly brain teaser
With Easter behind us the speediest eaters among you might be wondering how long you have to wait for another delivery of chocolate eggs. To complicate matters, Easter Sunday does not occur on a fixed date each year, but instead seems to move randomly around early spring, dependant on the whims of the moon. Is there any way of knowing which date Easter Sunday will occur next year? Or the year after? How about when it was 20 years ago?
This problem was tackled by Carl Friedrich Gauss, a man who had a particular interest in finding the answer. Gauss was born into a peasant family in Germany in 1777. As was relatively common at the time, his mother was unable to write and so did
not record the day of his birth. She was, however, able to remember that it was eight days before Ascension Day, which is 39 days after Easter Sunday. If Gauss could find the date of Easter Sunday in 1777 then he would be able to find his birthday.
Your challenge this month is to follow in Gauss’s footsteps and find the date of Easter Sunday 1777. Fortunately, saving you from going out and attempting your own lunar measurements, Gauss succeeded and published his method.
His approach was to search for the number of days, d, after March 22nd that the next full moon will occur in a given year and then the number of days, e, after that full moon that the next Sunday will occur.
He found that:
- d is the remainder you get when 19a-7 is divided by 30
- e is the remainder when 2b+4c+6d+3 is divided by 7
Where, if you use y as shorthand for the year, then:
- a is the remainder when y is divided by 19
- b is the remainder when y is divided by 4
- c is the remainder when y is divided by 7
Can you work out the date of Easter Sunday and so the date of Gauss’ birth?
Tap here for a hint Tap here for the answer
If you would like to get in contact with me about the puzzles or suggest a future puzzle for this column, please email me at maths.challenge@independent.co.uk
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