An empty trough has a balance point at its center. When the trough is full, its balance point is again at the center. Very skilled goldsmiths will pour gold dust into the trough from the left end and moving to the right. They will pack it to the left as they pour so that the gold resembles a loaf of bread with the Leading Edge as the gold's rightmost line. Before the trough is full, the gold dust will cause the balance point to move to the left. Consider these images to help visualize the situation:
We are interested in the conditions when the balance point is farthest to the left. Let's call that farthest left balance point the Leftmost Balance Point.
Here are some questions for you to ponder.
Question 1. Without knowing the weight of the trough when empty or the density of the gold dust, when the balance point is at the Leftmost Balance Point, will the gold dust have filled more than half the trough (i.e. will the Leading Edge be to the right of the center)?
Question 2. When the balance point is at the Leftmost Balance Point, where is the Leading Edge relative to the Leftmost Balance Point?
Question 3. If the gold dust density can vary due to heavy impurities in the first gold dust that is poured in, how does your answer to question 2 change?
Question 4. Given that the gold dust has a density of 10 gram per linear centimeter for the height and width of the trough, and that the trough is 20 centimeters long and weighs 300 grams, where is the Leftmost Balance Point?
You have until November 21 to wrestle with this puzzle before we post the answers.