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How to solve this puzzle? enter image description here

This puzzle is taken from the book The Ultimate IQ Test Book by Philip Carter and Ken Russell.

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Well

If everything's working, all lights are toggled twice

So the switch that isn't working is

The switch that toggles only 3/4, leaving them with an odd number of toggles. This is Switch D.

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  • $\begingroup$ Hmmmm, I suppose the real challenge is finding the catch.... Cause there must be a catch but no matter how hard I think, I cannot find one.... It seems hard to believe that something that could be solved by a 8 year old would be considered a "ultimate IQ test" $\endgroup$ – stack reader Nov 17 '16 at 15:12
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    $\begingroup$ It's only number 29. Maybe it ends up being that your IQ is the lowest number you don't get right. ;-) $\endgroup$ – Rubio Nov 17 '16 at 15:23
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I'll use a Truth table to solve it: $0$ representing off, and $1$ representing on. Note that the switches are basically inverters.

Initial State:

$[1,1,1,1]$
Apply $D$ $[1,1,0,0]$
Apply $C$ $[0,1,1,0]$
Apply $A$ $[1,0,1,0]$
Apply $B$ $[1,1,1,1]$
Real output: $[1,1,0,0]$
Bulbs $1$ & $2$ are correct. This likely means the bulbs that worked on them are working. I.e $A,B,C$ are working. $D$ should be the faulty one. I can verify this, by rerunning the sequence omitting $D$
$[1,1,1,1]$
Apply $C$ $[0,1,0,1]$
Apply $A$ $[1,0,0,1]$
Apply $B$ $[1,1,0,0]$
This gives us the final value.
$\therefore D$ is the faulty switch.
$Q.E.D$

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  • $\begingroup$ This answer was posted by Sconibulus several weeks ago. Please read other answers before making your own. $\endgroup$ – Deusovi Dec 6 '16 at 1:56
  • $\begingroup$ I used a Truth table. The question was trivial and if OP couldn't solve it I thought a more detailed explanation was in order. $\endgroup$ – Tobi Alafin Dec 6 '16 at 1:58
  • $\begingroup$ @Sconibulus' explanation doesn't hold for all cases(if a particular switch was made redundant) for example. So it is necessary to confirm suspicions with a Truth table. I thought this site was about puzzle solving. Why do I have so many downvotes. $\endgroup$ – Tobi Alafin Dec 6 '16 at 8:04
  • $\begingroup$ Because @Sconibulus' explanation is actually entirely complete and correct, requires no truth table to demonstrate, and was given long ago. (No switch is "redundant"; that is known from the puzzle itself.) This site is about puzzle solving—not puzzle re-solving. Stop trying to add answers where perfectly valid answers already exist. Between essentially saying OP is dumb for not getting this "trivial" question and saying, by adding your own equivalent one, that Sconibulus' answer is deficient, are you surprised people are downvoting you? $\endgroup$ – Rubio Dec 6 '16 at 10:31
  • $\begingroup$ I wasn't saying OP was dumb, nor the other was deficient. Just that my answer was more valid for a general case of the puzzle. If the OP applied the othee guy's answer to a more complex case, he might get it wrong. I felt the OP may need a better answer $\endgroup$ – Tobi Alafin Dec 6 '16 at 10:43

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