[Solution] Number 64 buttons from 0 to 63, and represent these numbers in binary, denoted as $000000,000001, \cdots, 111111$. On the $k$-th start, press the buttons whose $k$-th digit is 1 $(k=1,2, \cdots, 6)$, and record the $k$-th digit as 1 for the lights that turn on, and 0 for those that remain off. After 6 starts, each light will have a 6-bit binary number. Clearly, this 6-bit number is the number of the button that controls it. Therefore, 6 starts can solve the problem.

On the other hand, it can be shown that 5 starts are insufficient. Indeed, on the first start, no matter which buttons are pressed, at least 32 lights will be in the same on/off state. On the second start, at least 16 of these 32 lights will be in the same state. Continuing this process, by the fifth start, at least two lights will be in the same state. This means that these two lights will have the same state in all 5 starts, making it impossible to distinguish which button controls which light.
In summary, the minimum number of starts required is 6.
$13 \cdot 41$ Given that there are 64 light bulbs on the signal panel, each controlled by 64 buttons. Each light bulb is controlled by its own button. Each time it is activated, any group of buttons can be pressed, and the on/off state of each light bulb can be recorded. To figure out which button controls each light bulb, what is the minimum number of activations required?