What four weights can be used to balance from 1 to 30 pounds?
Answer
The four weights are: 1, 3, 9 and 17. The fourth weight is not 27 because by using a 27 pound weight, we would able to measure up to 40 pounds. But since we need to measure only up to 30 pounds, we can subtract 10 from 27 to get 17.
Let A=1, B=3, C=9 and D=17.
1lbs = A
2lbs + A = B
3lbs = C
4lbs = A + B
5lbs + A + B = C
6lbs + B = C
7lbs + B = A + C
8lbs + A = C
9lbs = C
10lbs = A + C
…
20lbs = B + D
…
30lbs = A + B + C + D