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The Ramsgate Sands

Thirteen youngsters were seen dancing in a ring on the Ramsgate sands. 

Apparently they were playing "Round the Mulberry Bush." 

The puzzle is this. 
How many rings may they form without any child ever taking twice the hand of any other child—right hand or left? 

That is, no child may ever have a second time the same neighbour.

See answer

Brain Teaser Of The Week