# Which node(s) does 16 connect with in this simple graph?

If we add 16 as a node to the graph below, which node(s) will it connect to?

Hint 1

the tag is indicating knowledge of computer science concepts, not external 'data' related to the graph.

Hint 2

This puzzle is derived from, but very much different from, another puzzle.

Hint 3

Nodes 8, 11, and 12 are not included because they are completely disconnected from each other and the other nodes from 0 through 15. They're still disconnected from the rest of the graph when we include 16.

Hint 4

The relation has something to do with comparing strings.

Hint 5

An edit distance (metric) is involved.

• Would including 8, 11, and 12 give too much away? Apr 22, 2020 at 17:37
• @RobPratt I've added information about those nodes as Hint 3 if you want it Apr 22, 2020 at 17:41
• Not a hint, but it looks like Big Hero 6 is waving at us. Apr 22, 2020 at 19:26
• If hint 4 is the case instead of the definition of simple graph(no loop) then I must say it should be connected with 15 as they have a long string :D
– m4n0
Apr 23, 2020 at 3:57
• Hint 4 and the definition of a simple graph are consistent. Cycles are allowed, but loops are not. Apr 23, 2020 at 4:01

## 1 Answer

Two nodes are connected if and only if

the English names of the numbers have Levenshtein_distance of 3. E.g. 'five' and 'four' - the f is the same, other letters have to be replaced. 'seven' and 'ten' - 1 letter needs to be replaced, 2 added or removed, so edit distance 3.

Therefore, 16 is connected to

13 ('sixteen' - 'thirteen') only; 15 is 'too close' with an edit distance of 2.