Math Puzzle: Ones and Twos
November 14th, 2008
| Categories: Logic, Math Puzzles
Here’s one that stumped me for a good twenty minutes before someone told me the answer … by the way, this is solvable by all readers, including bright high-school pupils. You don’t need to know how to use Lie derivatives on differentiable manifolds for this one.
What comes next in the following sequence?
1
11
21
1211
111221
As always, enjoy!
NOTE: SOLUTION ADDED, 19/Nov/2008
(browse comments to read it)
SOLUTION:
This is one puzzle you need to think verbally in. Just read the lines out loud, and observe the punctuation marks
one
one one
two ones
one two, one one
one one, one two, two ones
i.e., you’re just enumerating the number of ones and twos. Hence, the next line would be:
312211
Looking past the basic “gotcha” factor of this puzzle, it’s interesting to note that Google used it once on the Google Labs tests, as is shown on the following site:
http://cruftbox.com/blog/archives/001031.html
Interesting read. I’m not sure if it’s a hoax or not, or whether they still administer the same test. I think it’s a somewhat dumb test but maybe I’m just not part of the Google crowd …
’till next time!
I love your website - the puzzles are a great idea. This puzzle drove me crazy and I don’t feel so bad not getting it. I mean I know lateral thinking is highly valued these days but still! Also, I found your title a bit misleading, since it seems to imply that the sequence only involves ones and twos, ahem! I was disappointed over the summer when it looked like you were neglecting this blog - don’t ever stop!!
Hi Adrian,
Thank you for the kind words. I’ll try to keep updating the blog regularly. Since you have one yourself you should know that when you start these things you’re pretty sure you’ll attend to it properly, but then you find out how really demanding it is! But it’s still a lot of fun. I hope you keep on following it!
Assaf, I’m looking for some math insights on my blog post today. The post is related to the approach of virtual reality to “actual” reality using Crayon Physics computer programs as the example. Your recent work on physical based games will likely serve well.
My premise is that the closer virtual reality approaches “real” reality it’s “cool factor” increases. So a computer simulated system involving gravity, forces and rigid bodies is less “cool” when it is crude, clumsy and not realistic. The more realistic the system is, the higher it’s “cool factor”. I’m fascinated by even a simple physical system accurately replicated by a game (drop a CG ball, it falls, hits a box which tilts, etc…)
However, I am not as fascinated by dropping a real ball, watching it fall, hitting a real box which then tilts, etc… Why? Because the “Line of Real Reality” has been approached and crossed! This distinction could be demonstrated by posting two videos on YouTube and seeing which on gets more hits: CG ball drop or “real” ball drop. Nobody wants to see a real ball drop. Perhaps novelty plays a role.
But the substance of my math question is what happens when you graph this phenomenon? Put “Cool Factor” on the Y axis, and “Similarity to Reality” on the X axis. I have graphed two scenarios on my blog post: 1) The way it is; 2) The way it should be. I’m really interested in describing mathematically the function on this graph, especially immediately before, during and after the intersection of the line with a “Line of Real Reality”. Any of your thoughts, or thoughts of other members, would be greatly appreciated!
My mathematical tool box is a bit sparse. Cheers!