43. On the ray $(0,+\infty)$ of the number line, several (more than two) segments of length 1 are placed. For any two different segments, one can choose a number on each such that these numbers differ exactly by a factor of 2. The left endpoint of the leftmost segment is the number $a$, and the right endpoint of the rightmost segment is the number $b$. What is the greatest value that the quantity $b-a$ can take?
43. Answer: 5.5. Example: segments $[2.5,3.5],[4.5]$ and $[7,8]$.

Consider a number $x$ such that $x \in[a, a+1]$ and $2 x \in[b-1, b]$. Then $2 a+2 \geqslant 2 x \geqslant b-1$, from which $2 a+3 \geqslant b$. Next, consider any segment $[c, c+1]$, different from $[a, a+1]$ and $[b-1, b]$. Then $a<c<b-1$. Consider such numbers $y$ and $z$, that $y \in[a, a+1], 2 y \in[c, c+1] ; z \in[c, c+1], 2 z \in[b-1, b]$. Then $c+1 \geqslant 2 y \geqslant 2 a$ and $b \geqslant 2 z \geqslant 2 c$. Thus, $2 a+3 \geqslant b \geqslant 2 c \geqslant 2(2 a-1)=4 a-2$, from which $a \leqslant 2.5$. Therefore, $b-a \leqslant 2 a+3-a=a+3 \leqslant 5.5$.