Here is a problem
Notice in this video how the distribution of balls is incorrect
distribution of balls
So the problem is…
Can we determine from the given distribution produce by the triangle configuration what pegs of the triangle configuration are in the wrong place, assuming that the error is on the positioning of the pegs where the balls collide?
I think this should be solvable. But I also think is a really hard problem! Anyone care to solve it?
This is known as the Galton Board
in ideal situation (correct placement of pegs) perfect balls and other idealization should produce exactly a known distribution. Deviations from it means either the pegs are in the wrong place. Or many other problems. Assuming that the only possible misshape is the pegs been in the wrong position then what pegs are in the wrong position for this example?
Problem is that each ball hits each peg with a residual horizontal velocity. The theoretical distribution assumes each ball falls each way with probability 1/2. If the balls have residual horizontal speed then that is no longer a valid assumption.
Ok so from the final bucket where the ball gets to rest we should be able to determine the total sum of this residual horizontal velocities, right?
Would that not help in finding what is wrong with the positioning of the pegs alone the way?