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Fill the circles so that consecutive numbers are not adjacent Question
In each puzzle, fill the circles using all the positive integers 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.
Sample puzzle (n=7):
Sample solution:
Click here to reveal
Main puzzle (n=9):
1 answer
Answer
Solution method
First note the number of connections each node has.
Since the numbers at the end of the sequence have only one connection instead of two for inner numbers, place the end numbers in the two nodes with the most connections. That fixes 1 and 9.
Each of the 1 and 9 nodes are connected to all others except one. That forces 8 and 2.
You now have 3 4 5 6 7 left to place. The remaining nodes have 3, 6, 6, 3, and 4 connections. Therefore it makes sense to try placing 3 and 7 in the two nodes with 6 connections. Note that these can only go one way due to one of these nodes being connected to 2 and the other to 8.
Left to place are 4 5 6. The node at the very bottom touches both 3 and 7, so that node must be 5.
The remaining 4 and 6 can only go one way since one of the open nodes is next to 3 and the other next to 7.
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