Sunday, September 28, 2025

Scales problem

 I started by making the equation: a+b+c+d=40 because that would provide me with the largest value that we can make with the 4 weights. Then I decided that a<b<c<d. Then I walked down the list from the first equation.

Ex. 

a+b+c+d=40

b+c+d=39

a=1

b+c+d=38+a

a+c+d=37

b=3

Ect.

After following this for a bit I found that a=1, b=3, c = 9, and d=27.

at

1 comment:

  1. MaliheSeptember 29, 2025 at 12:28 PM

    You set a clear start with a+b+c+d=40 and the ordering a< b <c<d but the steps that follow ... read as conclusions without the missing reasons. Where does the two-pan feature (being able to place weights on either side) enter your argument? What makes
    a=1 necessary rather than a=2? What eliminates b=2 and forces b=3 . What principle generates d and guarantees no gaps from 1 to 40? And how do you verify that 1,3,9,27 truly reaches every integer in that interval, not just 40?

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