<img src="https://i.sstatic.net/viYBS.jpg" alt="outlet, 2 timers, bulb">
<br>
Two motorized 24-hour
[light timers](https://en.wikipedia.org/wiki/Time_switch)
are [daisy
chained](https://en.wikipedia.org/wiki/Daisy_chain_%28electrical_engineering%29)
between a power outlet and a light bulb.
For these timers, devise schedules and choose initial times
that produce the following lighting pattern
with the largest possible whole number $n$,
beginning when the outlet's power is switched on:

$~~~$  On for 1/2 hour,$~$ off for $n$ hours, <br>
$~~~~$ on for 1/2 hour,$~$ off for $n$ hours, <br>
$~~~~$ on for 1/2 hour,$~$ off for $n$ hours, <br>
$~~~~~~\vdots$


### If you are unfamiliar with these timers

Each timer repeatedly cycles through
its schedule of 24 intervals that last an hour apiece.
<br>
&bull;$~$ A circular dial determines the current point in the schedule
<br>
&bull;$~$ A motor rotates the dial to advance through its schedule
          whenever power is supplied to the timer
<br>
&bull;$~$ You may initially set the dial to any minute of any interval
<br>
&bull;$~$ You may preset each interval to ON or OFF
<br>
&bull;$~$ When the dial is in an interval that was set to ON,
          the timer becomes a direct connection for power to flow
          to whatever is plugged into the timer
<br>
&bull;$~$ When the dial is in an interval that was set to OFF,
          the timer does not provide a connection between
          what is plugged into it and what it plugs into

The first timer is plugged into the outlet.
<br>
&bull;$~$ It runs nonstop after the outlet is switched on
<br>
&bull;$~$ It supplies power&mdash;but only when its dial is in
          an ON interval&mdash;to the second timer

The second timer has the light bulb plugged into it.
<br>
&bull;$~$ It advances through its schedule
          only when the first timer supplies power
<br>
&bull;$~$ It lights the bulb, but only while powered by
          the first timer and when its dial is in an ON interval.