Problem Statement:
There are eight bags full of gold, one is not as full than the others. Using a pan balance scale, how can you figure out which is lighter than the others in the least amount of moves?
(Note that each comparison counts as a new weighing, even if some of the bags are the same as on the previous comparison.)
You Must:
Process:
I immediately realized you could do it in two, if you place them extremely carefully. For the first weighing you put four on each side, and wait to see which side is lighter. Then you take said lighter side and split it into two, placing each pair one the opposite sides of thier own pan (see picture below.)
There are eight bags full of gold, one is not as full than the others. Using a pan balance scale, how can you figure out which is lighter than the others in the least amount of moves?
(Note that each comparison counts as a new weighing, even if some of the bags are the same as on the previous comparison.)
You Must:
- Create a solution that will find the lightest bag.
- Explain how you can be sure that it will work.
- Explain how you know that there is no solution with fewer weighings.
Process:
I immediately realized you could do it in two, if you place them extremely carefully. For the first weighing you put four on each side, and wait to see which side is lighter. Then you take said lighter side and split it into two, placing each pair one the opposite sides of thier own pan (see picture below.)
Solution:
The set of bags that goes into the air is lighter, and the side it tilts to is heavier. Meaning that if the left side went up and dipped to the right, it would be the bag on the left side of the left scale. I know this will work because it is basic physics, but you must be very careful to place them in the same places or the balance will be off anyway.
Evaluation:
I believe that this problem was within the boundaries I would consider "easy" or "unworthy", I solved it and wrote this write-up within thirty minutes. I didn't need help from anyone and don't remember helping anyone. I did however enjoy it, and also enjoy harder versions of this type of problem. I would rate this problem a 5 of 10.