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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
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    $\begingroup$ @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
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    $\begingroup$ @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
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    $\begingroup$ @RosieF You are right, haven't thought of that. $\endgroup$ – npkllr Sep 18 at 9:40
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I think:

It's possible, if you go about it in the following unintuitive (and probably unintended) way:

 1. Make the first timer switch off/on at the exact same time (0 time elapsed between being on/off), or disable the off state entirely
 2. Make the second timer on for 2 hours: from 11 a.m. to 1 p.m., with a 24 hour cycle
Alternatively, do action 1 for timer 2, and action 2 for timer 1

   Due to Weather Vane's answer, it's clear that the first timer will influence the second, by altering the set of times for which the second timer will be active. The only way to prevent this (subtle?) alteration from eventually throwing one of the timers off-kilter is by having one timer be always on (i.e., with 0 delay between off/on times). After doing this, the other timer behaves as if it were plugged into a regular outlet (because the electric flow never shuts off).
   Then, how do we get an hour each in the mornings and evenings, with just 1 timer? Well, clearly, we have to use 2 adjacent hours, because we only have 1 effective timer at this point. So, we use 11 a.m. to 1 p.m. as the 2 adjacent hours, and that's that - every 24 hours, you will have exactly 1 hour of morning power, and 1 hour of afternoon power.

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  • $\begingroup$ Wow, that is sneaky. $\endgroup$ – waferthin Nov 4 at 15:19
  • $\begingroup$ @waferthin I agree :P $\endgroup$ – Avi Nov 4 at 15:21
  • $\begingroup$ This makes me laugh. $\endgroup$ – JL2210 Nov 4 at 15:58
  • $\begingroup$ @JL2210 Great :) $\endgroup$ – Avi Nov 4 at 16:06
  • $\begingroup$ Although the challenge does say "when required", so this doesn't really provide a solution. $\endgroup$ – JL2210 Nov 4 at 16:29
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I think you can. Say you have one timer going from 6 in the morning to 6 in the evening. Then you have another timer going from 5 in the evening to 7 in the morning. If these are plugged together in series, you would get this: First timer:


                 ______________________________________
 _______________|                                      |_____________________
 1  2  3  4  5  6  7  8  9  10  11  12  1  2  3  4  5  6  7  8  9  10  11  12
 
Second timer:

 __________________                                  ________________________
                   |________________________________|
 1  2  3  4  5  6  7  8  9  10  11  12  1  2  3  4  5  6  7  8  9  10  11  12
 
Combined:

                 __                                  __
 _______________|  |________________________________|  |_____________________
 1  2  3  4  5  6  7  8  9  10  11  12  1  2  3  4  5  6  7  8  9  10  11  12 
 

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  • $\begingroup$ For the first 6 hours, the second timer gets no electricity, so stands still. When the first timer switches on, the second timer will not switch off one hour later, but after 7 hours. $\endgroup$ – Jaap Scherphuis Nov 4 at 14:50
  • $\begingroup$ Oh. Forgot they're not on all the time. $\endgroup$ – JL2210 Nov 4 at 15:37

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