Five weights that measure everything up to 121
You have a two-pan balance. Reference weights may be placed on either pan, so a weight on the same pan as the object subtracts from the total on the other side.
Choose five weights so that every whole number of grams from 1 to 121 can be weighed exactly. Show that 121 is the most that five weights can reach, and explain how to weigh, say, 100 grams with your set.
Show a hint
Each weight can be on the object's pan, on the other pan, or unused: three possibilities. That suggests base three, and a set of weights whose sums and differences cover every number.
Your answer
Solving needs a free account
Answers, streaks and solutions unlock when you are signed in. Reading the question and the hint stays free.
Discussion
💡 Discussion rules
- No full solutions here. Hints and approaches only.
- Complexity, edge cases and intuition are the point.
- Interview experiences are welcome. Respect your NDAs.
Loading discussion…
Learn the concepts
The theory behind this question.