http://mathpuzzlewiki.com/index.php?action=history&feed=atom&title=Sequence_next_in_sequence 2026-04-04T15:17:28Z Revision history for this page on the wiki MediaWiki 1.44.0 http://mathpuzzlewiki.com/index.php?title=Sequence_next_in_sequence&diff=1378&oldid=prev 2017-07-25T13:10:46Z

<p>Created page with &quot;This sequence guessing puzzle hides a beautiful, well known sequence. ==Puzzle== What comes next: 1, 2, 2, 1, 1, 2, 1, ....? ==Help== {{Hint| Count the number of repeating...&quot;</p> <p><b>New page</b></p><div>This sequence guessing puzzle hides a beautiful, well known sequence.<br /> <br /> ==Puzzle==<br /> <br /> What comes next: 1, 2, 2, 1, 1, 2, 1, ....?<br /> <br /> ==Help==<br /> <br /> {{Hint| Count the number of repeating digits.}}<br /> <br /> {{Answer| 2}}<br /> <br /> {{Solution| This is the famous Kolakoski sequence (see the wikipedia page listed below). The sequence self-encodes the run length of repeated digits. These run lengths are 1, 2, 2, 1, 1, 2, 1,...., which is the sequence again. }}<br /> <br /> ==Bonus==<br /> <br /> Find a sequence using the numbers 1, 2, and 3 that has the same property as the one above.<br /> <br /> ==References==<br /> <br /> [https://en.wikipedia.org/wiki/Kolakoski_sequence Wikipedia page] (contains spoilers).<br /> <br /> [[Category:Short puzzles]]<br /> [[Category:Sequences]]<br /> <br /> __NOTOC__</div>

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