riddle/puzzle

I am almost certain this is impossible (would love to be proved wrong though!)

If I understand it correctly (none are allowed any immediate neighbours in a 5x5 grid) then the most you can have is 9 dots, like this:

Code:

 ———————————
| * - * - * |
| - - - - - |
| * - * - * |
| - - - - - |
| * - * - * |
 ———————————

 

You cannot physically pack the dots any tighter together than how I placed them so 9 is the absolute maximum possible for a 5x5 grid.

I suspect whoever is telling you this is possible is having a little joke at your expense

 

this^^ the grid is at its maximum the way its arranged. Its not possible.

Next one for you is: you have three houses and three utilities(water, gas, electricity). Can you connect all the utilities to all the houses without crossing the lines.

 

Nice one ;-) And Taken when you've solved Walsh06's puzzle (lots of luck!) here's one that I always enjoy giving people (I can assure you that this genuinely IS possible):

You have three pencils of equal length in front of you on the table in the shape of a triangle. Add three pencils to this triangle to make FOUR triangles.

Rules:

1. You can not move any of the three pencils that you start with
2. All six pencils are the same length, and you can not break any in half
3. All four triangles should be equilateral (all angles are 60º)
4. Only create four triangles, no more, no less

Please don't reply with the solution here without using

Spoiler

[ spoiler ]

in case others want to get it themselves!

 

Anyone actually stuck on the six pencils puzzle I'll give you a tip: you are far more likely to find the solution if you actually get six pencils (or pens, or matches or whatever) and try it than by merely thinking about it.

I like this one a lot because it really does genuinely test your ability to think outside the box (to use a rather overused cliché)

 

Note there will be exactly four triangles, no more, no less. And all four are the exact same shape, and all are equilateral (meaning all angles are 60º)
(actually I'd better edit the rules )

 

Yes indeed, that's exactly it