Question 75
On a white strip that is $100$ mm long and $10$ mm wide, ten black squares are drawn that, from left to right, have sides of length $1$, $2$, $\ldots$, $10$ mm. The centre of each black square is in the middle of the strip and $5$, $15$, $\ldots$, $95$ mm from the start (left edge) of the strip.
A transparent square is moving along the strip from left to right (indicated in grey). In the figure, two possible positions of the transparent square are depicted: in the first, its left edge is $21$ mm from the start of the strip, and in the second, it is $54$ mm from the start of the strip. In both cases, less than half of the part underneath the square is coloured black (only $9\%$ in the first case). There is one position in which exactly half of the part of the strip underneath the square is coloured black.
Determine, for that position, how far the left edge of the square is from the start of the strip.
A transparent square is moving along the strip from left to right (indicated in grey). In the figure, two possible positions of the transparent square are depicted: in the first, its left edge is $21$ mm from the start of the strip, and in the second, it is $54$ mm from the start of the strip. In both cases, less than half of the part underneath the square is coloured black (only $9\%$ in the first case). There is one position in which exactly half of the part of the strip underneath the square is coloured black.
Determine, for that position, how far the left edge of the square is from the start of the strip.