This is a puzzle that ran for three weeks in September 2015. The idea was to work out the rule for a sequence, with a new term given each day.
Although the puzzle was solved after twenty-two terms had been revealed, I have provided thirty-one terms below. I think that this gives the best chance of finding the solution for anyone else who wants to have a go.
Here is a sequence:
1 1 2 1 2 2 2 1 2 2 2 2 2 2 3 1 2 2 2 2 2 2 3 2 2 2 3 2 3 3 3 …
Each day, the next term in this sequence will be revealed.
Your challenge is to determine the rule governing the sequence.
The sequence challenge has been solved!
Click here for the solution.
Here is an Excel version of the sequence for ease of reference:
The sequence follows a moderately straightforward mathematical rule and all the terms are non-negative integers. I don’t know how difficult it will be to work out; fairly tough I think, but who knows. Perhaps someone will get it straight away, perhaps we will still be going in a year’s time. I don’t think the answer is searchable, but if it is then I may end up looking rather silly.
In mathematics, there can often be several different but equivalent ways of saying the same thing. For this reason, any proposed rule that would generate the complete correct sequence will be considered a correct solution. The rule does not have to be phrased in precisely the way that I have in mind.
As an added incentive, a Mystery Science Prize* is available** for the first person to post the correct answer in the comments below. Only one guess per person per day, please; i.e. you can’t guess again until the next term is released.
UPDATE 11/09/2015: cinnamon_carter has generously pledged 15000 units of crypto-currency to the winner, alongside my prize. I don’t really know much about this, so for further details, start from this comment and this tweet.
* Don’t get too excited. It is worth under £10 and that was when it was new.
** Provided that you can later provide me with a valid postal address to a sensible location (No Antarctic survey bases or remote Pacific atolls, please. I reserve the right to duck out of ludicrously high postage costs.) and that the postal service successfully deliver it to you.
Bonus points are awarded each day for anyone who correctly guesses the following day’s term (in a reply to my latest tweet).
FINAL LEADERBOARD (19/09/2015)
Troy R – 11 pts
Jesse Thompson – 9 pts
Aaron Percival – 8 pts
John G – 7 pts
Michael Bench-Capon – 6 pts
Brad Smith – 3 pts
BurHanSolo – 3 pts
Chris Purcell – 2 pts
Alexander – 1 pt
Aoife Hunt – 1 pt
Gareth Adams – 1 pt
Henry W McLaughlin – 1 pt
H J – 1 pt
Ignacio Mancera – 1 pt
John Doe – 1 pt
Luke – 1 pt
Matthew Jackson – 1 pt
mike – 1 pt
Myria – 1 pt
Nick T – 1 pt
Simon Capstick – 1 pt
Timo – 1 pt
Tom Flowerdew – 1 pt
Thomas Oléron Evans, 2015