Consider a lamp whose switch is controlled by a sophisticatedtimer. At the start

Question

Consider a lamp whose switch is controlled by a sophisticatedtimer. At the start of the experiment the lamp is switched on, andremains on for exactly one minute. At the end of that minute, thetimer switches the lamp off. It remains oft for half a minute, andthen is switched on for 15 seconds, then off for 7.5 seconds, thenon for 3.75 seconds, and so on. Each period in which the lamp is on(off) for n seconds is followed by a period in which the lamp isoff (on) for n/2 seconds.
At the end of 2 minutes: (i) how many times has the lamp beenswitched on and off? (ii) is the lamp now on or off?

Explanation / Answer

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