Question 13
A car racing track consists of 6 circles $\Gamma_1, \Gamma_2, \Gamma_3, \Gamma_4, \Gamma_5$ and $\Gamma_6$, interior tangents at a point $P$. The lengths of the circles are 1 km, 2 km, 4 km, 8 km, 16 km and 32 km, respectively. Two pilots, $A$ and $B$, travel along the track as follows: starting at point $P$, pilot $A$ travels $\Gamma_1$, when it reaches $P$ again it travels $\Gamma_2$, then travels $\Gamma_3$, until which completes the entire track route and reaches $P$ again. There the whole journey begins again, over and over again. It travels all the time at a constant speed, and travels through each of the circles in the same direction. Pilot $B$ begins his trip somewhat later than $A$, and travels through the circles $\Gamma_1, \Gamma_2, \Gamma_3, \Gamma_4, \Gamma_5$ and $\Gamma_6$ in the same order as $A$, at the same speed as $A$, but always in the opposite direction to that of $A$.
Suppose $B$ knows the time at which $A$ started its journey. Decides whether $B$ can choose the start time of its own course so that the two cars never pass each other on the track.
Suppose $B$ knows the time at which $A$ started its journey. Decides whether $B$ can choose the start time of its own course so that the two cars never pass each other on the track.