Question

As part of his effort in promoting innovation and healthy relationship among all the employees working in different locations (branches), Andrus started an annual activity where groups of employees (based on location) compete to pitch their most extreme ideas to one another. Each group would present their ideas, then the branches vote one by one. (They are not allowed to vote for their own branch) Each branch awards 8 votes to their favorite, 4 to the second, 2 to the third and 1 to the fourth. Clearly, tactical voting is important, so the order of voting is changed every year. This year, the branches vote in order from most northerly to most southerly. The results before the last two branches have voted are shown below (in voting order). Who still stands a chance of winning? Walk me through your entire thought process! (30 points)

Branch	Total Score
Fartown	6
Greenport	5
Longwood	6
Watertown	24
Giggles Town	12
Black Stones	9
Martinsville	24
South Peak	4
Riverton	13
Runcastle	17

Answer 1

The results before the last two branches have voted are shown (in voting order). it means that Riverton and Runcastle are yet to cast their votes. result shows that highest score till this voting stage is 24 which is achieved by Watertown as well as Martinsville.

now to become a winner either of Riverton and Runcastle must achieve more than 24 score.

Who amongst Riverton and Runcastle still stands a chance of winning can be determined by considering maximum possiblity of scoring

possibility1: if Riverton awards 8 votes to Runcastle then,

new total score of Runcastle = earlier score + 8

= 17 + 8

= 25

since 25 is greater than 24 hence Runcastle has a chance of winning if Riverton awards 8 votes to Runcastle.

possibility2: if Runcastle awards 8 votes to Riverton then,

new total score of Riverton = earlier score + 8

= 13 + 8

= 21

since 21 is lesser than 24 hence Riverton has no chance of becoming winner.