Submitted by vc124 on Thu, 11/24/2016 - 21:15
Forums:
Why do you have to take off 1 to get rid of the 0 if the task says including zero ounces? Shouldn't you rather add 1 so you don't get a 1/2 case for 0 after dividing by 2?
Submitted by vc124 on Thu, 11/24/2016 - 21:15
Why do you have to take off 1 to get rid of the 0 if the task says including zero ounces? Shouldn't you rather add 1 so you don't get a 1/2 case for 0 after dividing by 2?
© 2024 University of Cambridge
non zero
I assume you're talking about the hints and partial solutions sheet.
Yes, the given solution shows how to find the number of distinct non-zero weights you can measure, so to give the answer including zero you would have to add one at the end, which is equivalent to adding an extra 1 and dividing by two as you suggest.
It's worth considering why it's not possible to weigh $3^n$ different weights and you can only manage approximately half that many - this problem which is structurally similar might be of interest: http://wild.maths.org/longer-and-longer