Originally Posted by

**godelproof** I'll post my opinions for Q1. Check to see if there's any problem...

-------------------------------------------------------------------

Consider the configuration $\displaystyle ({a}_{1},\ {a}_{2},\ {a}_{3},m,L)$. Without loss of generality, let $\displaystyle {a}_{3}>{a}_{2}>{a}_{1}$. Let $\displaystyle {a}_{3}<m$ (otherwise no feasible plan exists).

Conjecture: Let the motorcycle go straight to $\displaystyle {A}_{1}$ and carry him forward to catch $\displaystyle {A}_{2}$. A feasible plan exists *if and only if *the motorcycle is able to catch $\displaystyle {A}_{2}$ before or just when she reaches Y.

If the motorcycle **just** catches $\displaystyle A_2$; by that time A3 has already finished the journey since, $\displaystyle {a}_{2}<a_3$

Is the above conjecture true?

If it is, then $\displaystyle {\mathbb{B}}^{5}$ looks like this:

$\displaystyle {\mathbb{B}}^{5}$={$\displaystyle ({a}_{1},{a}_{2},{a}_{3},m,L)|m>{a}_{3}>{a}_{2}>{a }_{1},\ 2{a}_{2}\leq{a}_{1}+m$}.

An illustration is given below for m=10. For any m, just shift the the blue lines up or down.