Where to place your digit

I first came across this clever puzzle in Martin Gardner's excellent book "Further Mathematical Diversions". It had been used to illustrate the fact that by using a logical approach it is possible to quickly derive a solution to a problem that would be difficult to solve by a brute force method - such as that which might be tried using a computer - of trying every one of the 40,320 possible arrangements until the unique solution (apart from upside down and mirror image forms) was found.

The puzzle


The digits from 1 to 8 are to be placed in the eight circles shown in the figure above. There is one condition that must be kept and that is that no two digits that are next to each other in serial order may go in circles that are directly connected by a line. So if 5 were placed in the top circle then neither 4 nor 6 may be placed in any of the three circles that form the horizontal row beneath it.

Click here for the solution.

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