Due November 8

This problem can be solved by trial and error, but there are some patterns and rules that a clever person can deduce. We consider this to be an medium problem, worth 15 points. Send answers and questions to mathstat@uoguelph.ca

Your goal is to make the highest possible score in the following game. You have a collection of numbers 1, 1, 1, 2, 3, 5, 6. A move in the game is made by picking any two numbers and either adding them or multiplying them. The result is put back into the collection. You continue moving until one number is left. That number is your score.

Example:

CollectionMove
1,1,1,2,3,5,61+6=7
1,1,2,3,5,71+5=6
1,2,3,6,71+2=3
3,3,6,73*6=18
3,7,183*7=21
18,2118*21=378
Score=378

To mail back the answer above you could e-mail us the mesage (1+6)*(1+5)*(1+2)*3=378 to show how you got the answer. The best possible score is bigger than 378. Send your answer to mathstat@uoguelph.ca

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