## Why the hot light bulb annoys me

The light bulb puzzle presents you with three switches, one of which controls a light bulb inside a closed room. You are permitted to flip switches as much as you like, then you must open the door and say which switch controls the light bulb.

You don’t seem to have enough information. You can flip one switch and open the door. If the light is on then you have found your switch. However, if the light is off you can’t tell which of the other two switches controls the bulb.

The solution is to first flip a switch on for ten minutes, then off again. Now flip a second switch on and open the door. Leaving the light bulb on for ten minutes would allow it to heat up. Then, if the light is on or off and hot, you know which of these two switches was the cause. If the bulb is off and cold, you can identify the third switch.

This puzzle annoys me, but I was not sure why.

I heard the following as a “grammar test”: which is correct, “the yolk of an egg is white” or “the yolk of an egg are white”? The answer was given as: “don’t be silly, the yolk of an egg is yellow”. This annoyed me because it was set up as a grammar test so I took the incorrect yolk colour to be a mistake in the statement of the problem that was safe to ignore, restraining myself to the grammatical aspect.

Here is another puzzle, a sorites. Sorites were included by Lewis Carroll in his book Symbolic Logic (1897). Your task is to arrange the following logical statements into a chain to draw a conclusion.

1. babies are illogical;
2. illogical persons are despised;
3. no one is despised who can manage a crocodile.

In this case, since babies are illogical, illogical persons are despised and despised people cannot manage crocodiles, we conclude: “babies cannot manage crocodiles”.

I have presented this to someone who said that the result is obvious since of course a baby cannot manage a crocodile. However, there is no requirement for the statements in a sorites to be true. Are illogical persons, including babies, really despised? This is a logic puzzle in which the question of whether a baby could manage a crocodile in reality is not relevant.

For me, saying “don’t be silly, the yolk is yellow” is like saying “of course babies can’t manage crocodiles”. You have been placed in the constrained reality of the puzzle and it is irritating to allow extra information from outside of the puzzle. In the light bulb puzzle we have switches that cause lights to illuminate. The fact they also cause the bulb to heat up is a fact from the real world intruding on the world of the puzzle. You might equally well say “flip each of the switches and look at the crack under the door to see if any light comes out” or “why are there three switches, anyway?”

Is there a way to fix the puzzle to remove the irritation? Mentioning in the statement of the puzzle that the bulbs heat up would give the game away, while not mentioning it situates the solution outside the constrained reality of the puzzle. Consequently, this cannot work as a viable puzzle.

That is why the hot light bulb annoys me.

1. I gave this as a talk at the Maths Jam Conference 2011.

Laurie Brokenshire told me he had heard the light bulb puzzle presented as a “Lateral thinking puzzle”. This changes the situation and I think makes the puzzle viable. Being told this is a lateral thinking puzzle means you are specifically being told to bring in extra information from outside the statement of the puzzle.

Tony Mann told me he likes the puzzle as stated because it separates mathematicians (who cannot solve it) from engineers.

Friday, January 20, 2012 at 10:56 pm | Permalink
2. Andrew wrote:

I had a similar feeling recently with the knight/dragon/numbered poisoned wells puzzle: the solution involves inferring in-world rules that you aren’t given, but being given them would make it too easy. In that case, I think the solution is to phrase the puzzle very carefully (like using “lateral thinking” in place of “logic”) but it’s a problem in general because you can’t tell if a puzzle’s brilliant or rubbish until you’ve spent hours thinking about it, given up, and asked someone.

Friday, January 20, 2012 at 11:18 pm | Permalink
3. I agree about Peter’s puzzles, but I’d like to defend the poisoned-wells puzzle. I was told the rules very clearly and still didn’t get it for a while. It requires a good kind of lateral thinking.

Saturday, January 21, 2012 at 8:10 am | Permalink
4. John N wrote:

I, too, find this “puzzle” very annoying due to crucial built-in assumptions.

Assumption 1: The bulbs give off noticeable heat. Hopefully this puzzle will be outmoded as LED lighting comes into play.
Assumption 2: The bulbs are reachable. Nothing indicates the bulbs aren’t high overhead.

Sunday, January 29, 2012 at 5:19 pm | Permalink