Puzzle 42 | (Placing the numbers)

Place the numbers 1, 2, 3, 4, 5, 6, 7, 8 into the eight circles in figure given below, in such a way that no number is adjacent to a number that is next to it in the sequence.For example 1 should not be adjacent to 2 but can be adjacent to 3, 4, 5, 6, 7, 8. Similarly for others.

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Trivial Solution:

Trying for 8!=40320 combination would be tedious task.

Smart Solution:

• The easiest numbers to place are 1 and 8, because each has only one number to which it cannot be adjacent, namely, 2 and 7, respectively. ?
• The hardest circles to fill are those in the middle, as each is adjacent to six others.

This suggests that we place 1 and 8 in the middle circles. If we place 1 to the left of 8, then the only possible positions for 2 and 7 are shown figure below:

?

The number 3 must now be placed on the left-hand side of the diagram, and 6 must be placed on the right-hand side.

Now it is easy to place all the remaining number as shown in figure below:

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