### Brain Teasers

# Circular Socket

Mad Ade has just purchased himself a second hand Automatic kebab rolling machine (made in Madadia, at the world famous "Botulism Bros." factory). At the back of the machine is an electrical cable with a quite strange plug. The plug has 7 prongs arranged in a circle, which matches the socket on the wall, thus allowing the plug to be rotated and inserted in 7 different ways. Each prong of the plug is numbered from 1 to 7. The holes in the socket are also numbered, but can be switched around. To make the Kebab machine work only one plug prong has to fit in the corresponding hole of the socket. How can Mad Ade Number the socket holes in such a manner that no matter how the plug is inserted, at least one prong will fit into the correctly numbered hole in the socket?

### Answer

The prongs on the plug are already marked with consecutive numbers: 1, 2, 3, 4, 5, 6, 7. Number the holes in the socket clockwise, with every other number, then wrapping back around: 1, 3, 5, 7, 2, 4, 6. This ensures at least one correct connection no matter how the plug is inserted.Hide Answer Show Answer

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## Comments

There are lots of solutions to this one.

Solutions that keep pin 1 fixed in the unrotated position

include: "1357246", "1473625", "1526374",

"1642753", and "1765432". These correspond

to s=1+((p-1)*a mod 7), where s is the socket number,

p is the position, and a is 2, 3, 4, 5, or 6, respectively.

Variants of these leave other pins fixed in the

initial position.

Solutions that keep pin 1 fixed in the unrotated position

include: "1357246", "1473625", "1526374",

"1642753", and "1765432". These correspond

to s=1+((p-1)*a mod 7), where s is the socket number,

p is the position, and a is 2, 3, 4, 5, or 6, respectively.

Variants of these leave other pins fixed in the

initial position.

I never said that there was only one answer, that was just the first one I found that fitted.

Sure, but I consider multiple answers to be a defect in a teaser, unless either the teaser or the answer allows for the possibility.

Whether it's a big defect or a little defect depends on the teaser, and how dense the solution space is, and also on how hard it is to force (or prove) uniqueness.

For example, if I said "My house number is even - what's my house number?," that would make a pretty crappy teaser, because

there are so many possible correct answers and they are trivial to find.

Ideally, the solver should be able to take a correct answer, look at the official answer, and see that either

his/her answer fits, or that the official solution is "better" in some way that the one he/she got.

In this case, it's not a huge defect, and it's hard to prove completeness - I don't know if there are other

solutions beyond the 35 that I found (the five listed, plus their tranformations by leaving one of the other 6 pins

fixed). But I think an answer that acknowledges at least those 35 possibilities is better than just giving one answer and leaving

it at that. It's still a fun and clever teaser, though, even with the defect.

Whether it's a big defect or a little defect depends on the teaser, and how dense the solution space is, and also on how hard it is to force (or prove) uniqueness.

For example, if I said "My house number is even - what's my house number?," that would make a pretty crappy teaser, because

there are so many possible correct answers and they are trivial to find.

Ideally, the solver should be able to take a correct answer, look at the official answer, and see that either

his/her answer fits, or that the official solution is "better" in some way that the one he/she got.

In this case, it's not a huge defect, and it's hard to prove completeness - I don't know if there are other

solutions beyond the 35 that I found (the five listed, plus their tranformations by leaving one of the other 6 pins

fixed). But I think an answer that acknowledges at least those 35 possibilities is better than just giving one answer and leaving

it at that. It's still a fun and clever teaser, though, even with the defect.

I understand your point of view, but just how long would this teaser be if every single answer was included. Indeed how cluttered would the site become with all this surplus information. I don't see that putting only one answer is a bad thing, especally if it encourages people to re-read the teaser and think "I bet I can find more". Many people on this site spend meer seconds viewing teasers before clicking for the answer, and then typing comments such as "easy", "it took me ten seconds" and other such rot. I can tell that you are not one of those, you have took the time to examine, question and explore the teaser. If every one was like you, then I would try and include every answer, but sadly, at the present it is a great deal of work for nothing.

Yeah but what you could have done was made the puzzle harder by saying 1 isn't beside 2 or something like that so you could logically work down to only one solution.

I did this puzzle as a kid, and its pretty easy to gues, even if you don't understand whats going on. But then I saw the same type narrowed down to one solution in a really good logic puzzle.

I did this puzzle as a kid, and its pretty easy to gues, even if you don't understand whats going on. But then I saw the same type narrowed down to one solution in a really good logic puzzle.

It seems to me that the easiest solution to this teaser is to simply number all the socket holes as a 1. Or all as a 2 or 3, etc. Then one of them will have to match no matter what.

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