In each puzzle, fill the circles with the numbers 1, 2, 3, ... n, where n is the number of circles in such a way that consecutive numbers are NOT in circles that are joined with a line.

I designed all the puzzles in this set except the first one. I don’t know where I found that particular puzzle.

8 circles #1

8 circles #2

8 circles #3

9 circles

10 circles


1 Answer 1


Like the previous puzzles of this type, we can use a certain strategy to break into these puzzles logically:

puzzles with yellow circles

Each of the yellow circles is connected to every other circle in the puzzle but one. So the yellow circles have to be the "endpoints" of the chain, and their non-neighbors are the numbers next to the endpoints:

puzzles, each with circles filled in

From here, it's easy to solve the puzzles:

solved puzzles

  • $\begingroup$ Good answer, except you made a mistake in my 2nd puzzle. $\endgroup$ Jun 4, 2022 at 0:51
  • $\begingroup$ @WillOctagonGibson Fixed, thank you! $\endgroup$
    – Deusovi
    Jun 4, 2022 at 0:53
  • $\begingroup$ Unfortunately, it’s still wrong. $\endgroup$ Jun 4, 2022 at 0:57
  • $\begingroup$ @WillOctagonGibson Fixed for real this time! (Counting from 1 to 8 is hard...) $\endgroup$
    – Deusovi
    Jun 4, 2022 at 0:58
  • $\begingroup$ Note that for n=8, after placing 1,2,7,8, the remaining empty cells match the problem n=4 from the set #1. Likewise for n=9, after placing 1,2,8,9, the remaining white cells match the problem for n=5. $\endgroup$
    – Florian F
    Jun 4, 2022 at 14:32

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