HDRDTD wrote:

: If you look at it as each box sites on two segments, and count that way, or
: in other words if each segment was shown as the width of a box, the the
: ratio appears as 3:1 which provides the correct solution.

No, then the ratio is 2.5 : 0.5, or 5:1, because the center of one
weight is halfway through the 3rd double segment, and the center of
the other weight is halfway through the first double segment.

I think it's clearer if you use circles or triangles to represent the
weights, so it's more obvious where the weight "is".

Or, think of each side as having two weights, each one segment wide
and half the total weight. You can treat the total weight as being at
the midpoint between the two weights, but you clearly can't ignore the
position of one weight and treat the total as being at the end of the
other weight.

--- Chip