Assume you have nine coins, one of which is counterfeit and weighs less than the other eight coins. Diagram the least number of weighings required to absolutely determine which of the nine coins is counterfeit as a tree. Indicate a scale as a line with numbers on the left and right indicating the number of the coin being weighed. Under the scale indicate the number of the counterfeit coin in position with a circle around it. For example, weighing coins numbered one and two on the left and eight and nine on the right is diagrammed as