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Imagine we have some simple mechanical 24 hour wall timers like this:

There’s one restriction though, they’re badly designed so each one can only turn on once and turn off once in a 24 hour period (but you can set the times of each).

If I (possibly insanely!) stack them by plugging them into each other can I use them to turn a light on in the mornings (for say an hour) and on in the evenings (for an hour)?

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My answer is

No!
You can only use a stack of these timers to turn a light on less often.
The reason is, the clock on this type of timer is mains powered and not battery powered.
So the second timer doesn't run at all when the first timer is off.

For example, suppose the base timer is set to be on for 12 hours.
And the next timer is set to be on for 6 hours.
Then the second timer will be on every other day.

    ____                             ____
   |    |                           |    |
 __|    |___________________________|    |_________
 0 3    9 12      12      0       0 3    9 12     12

  ________         _______         ________
 |        |       |       |       |        |       |
 |        |_______|       |_______|        |_______|
 0        12      0       12      0        12      0

For the question: the timing can be achieved on the first day only.

For example, suppose the base timer is set to be on for 13 hours: on at 0, off at 13.
And the next timer is set to be off for 11 hours: on at 12, off at 1.
  _       _       _______                __
 | |     | |     |       |              |  |
 | |_____| |_____|       |______________|  |______
 0 1    12 13    13      1 2     2     12  15   15 

  _________       _________       _________
 |         |     |         |     |         |     |
 |         |_____|         |_____|         |_____|
 0         13    0         13    0         13    0

As can be seen, it goes wrong on the second day:
On the first day the light is on for two 1-hour periods.
On the second day the light is on for one 12-hour period.
On the third day the light is on for one 3-hour period.

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  • 2
    $\begingroup$ Quite right. It is all too easy to overlook the fact that the timers influence each other. $\endgroup$ – Jaap Scherphuis Sep 18 at 9:16
  • $\begingroup$ But you can connect them in parallel (not series). $\endgroup$ – trolley813 Sep 18 at 9:34
  • 3
    $\begingroup$ @trolley813 perhaps, but the question says "stack them by plugging them into each other". $\endgroup$ – Weather Vane Sep 18 at 9:46
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    $\begingroup$ What if you stacked a third one, could you get it to work for the 2nd day? Then logically a 4th one for the 4th day and so on? Just theoretically. $\endgroup$ – waferthin Sep 18 at 9:53
  • 2
    $\begingroup$ @waferthin I suspect that you can get it to work for the first n days before it all breaks down, by using n+1 clocks, but the length of time that the lights are on gets smaller for larger n. I haven't quite worked out the details. $\endgroup$ – Jaap Scherphuis Sep 18 at 12:19
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Edit: As Weather Vane's answer shows, the following only works with battery powered timers.

That should be easy by stacking two of the timers.

The first one is turned on at 19 and turned off at 8.
The second one is turned on at 7 and turned off at 20.

x -> on
- -> off
...........1..2
0-7......x..-
7-8......x..x
8-19.....-..x
19-20..x..x
20-0....x..-

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  • 3
    $\begingroup$ This is wrong, as Weather Vane's answer shows. $\endgroup$ – Rosie F Sep 18 at 9:32
  • 1
    $\begingroup$ @RosieF You are right, haven't thought of that. $\endgroup$ – npkllr Sep 18 at 9:40

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