You have three houses or squares drawn on paper and below them Three smaller squares representing gas, water, and electric.  Can you draw a line and get each utility into every house (9) total lines, without crossing over any line?
 
 
 
 
 
 

                THE SOLUTION

Without the drawing being 3D this puzzle cannot be done. Many people say it can but using the drawing above it cannot. The best result you may get is only eight proper connections. Other variations of the puzzle can be found below.  People who are much brighter than I can explain better so here is what some of them say about the puzzle.

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1. The only way this can be done without the lines crossing is by allowing one of the lines (it doesn't matter which one) to enter a house then emerge from the house on the other side of the house when it will be able to enter another house without any other line having to be crossed.
   Keep on sending out the quizzes: you give a lot of people a whole heap of pleasure.
   
       Regards,           Neil Phillips

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2. It is known as the Turan Brickyard Problem.  The formula says this let n = the number of houses and m = the number of utilities.  Then the minimum crossing number is known by the formula 
 Cr(n,m) = [n/2] [(n-1)/2] [m/2] [(m-1)/2] where [x] denotes the integer part of x. 
 So the minimum crossing number of Cr(3,3) = [1.5] [1] [1.5] [1] = 1 * 1 * 1* 1 = 1. 
 So they can NOT be connected without crossing. M. Adair

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3. (This puzzle is a classic one which has no solution in 2D. However, if you place the items on a doughnut shape in 3D you can solve it. )

      regards             Lisa Belfield

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4. Based on the statement that 'drawn on paper' implies that this is a 2D surface then one can NOT connect the 3 utilities to the three houses.  I am searching for a source for this but haven't found one.  It is related to the mathematical "Four Color Map Theorem" but I can't find the exact source. 

Were you to change the wording and state that the surface was not 2D but say a 3D Sphere then the answer is yes.

-Mike