# Mr. Sloane's Tree

Mr. Sloane is a man that likes to draw trees with dots.

Give him two dots and he'll draw you one tree, but give him three and he'll draw you no tree.

How many trees can he draw with 6 dots? and with 11 dots?

• Is this YouTube video related? – Mr Pie Aug 31 '18 at 14:06
• @user477343 it isn't sorry! – Luis Sousa Aug 31 '18 at 15:28
• @LuisSousa, which one of the answers provided by Gareth McCaughan is correct? – El-Guest Aug 31 '18 at 15:39
• @El-Guest the second one, can you guess the inspiration for this (failed) puzzle? – Luis Sousa Aug 31 '18 at 15:47
• Is there a special event/milestone happening with OEIS this week/today? I'm not at all familiar with what it might be, @LuisSousa unfortunately! – El-Guest Aug 31 '18 at 15:52

Here are some possible answers. They all

allow us to take "Mr Sloane" to be N J A Sloane, creator of the Online Encyclopedia of Integer Sequences, "trees" to have its graph-theoretic sense, and "dots" to refer to the vertices of the trees.

First:

Mr Sloane likes to draw series-reduced planted trees, sequence A001678. In this case the numbers we need are 2 and 35 respectively.

Second and simpler:

Mr Sloane likes to draw series-reduced trees, sequence A000014. In this case the numbers we need are 2 and 14 respectively.

Third:

Mr Sloane likes to draw trimmed trees, sequence A002988. In this case the numbers we need are 2 and 39 respectively.

Unless the intended answer fits the given statement markedly better than all of these (or is one of these and fits markedly better than the other two for some reason), I think we need some further information if the puzzle is to have a definite correct answer.

• You're right, with the information given all your answers fit in. Guess i should've formulated my question better, was thinking of providing a drawn tree initially but didn't want to give away too much information. – Luis Sousa Aug 31 '18 at 15:40
• Your second answer is the correct one, i could edit my post to present a drawn tree from a n number of nodes to guess the right sequence but i think it would be trivial now. – Luis Sousa Aug 31 '18 at 15:45

• This is a good point, and would make this a basic calculation which by the standards here is not a riddle. I based my answer on the pattern and number-sequence tags, which again point back to basic calculations. I'm not sure a direct correlation between the trees and dots can be deducted from the supplied information. – Taco Aug 31 '18 at 15:05
• There's also the geometry tag. Again, if it's not possible to figure out what's up with the trees and the dots then I think the puzzle is hopeless. – Gareth McCaughan Aug 31 '18 at 15:12