HOME Our Zones Game Downloads Not To Be Missed Games Puzzles Site Of The Week Information

Daily Puzzles Updated 7x a week











Daily Brain Teaser Challenge
Daily Trivia Challenge
Daily Puzzle Zone
Daily Random Puzzle
Daily Trivia Quiz #1 #2
Classic Sudoku #1 | #2
Daily Fun Zone Newsletter
Kakuro
Mindsweeper
Akari
Tatami
Classic Crossword Puzzle
British Version Crossword
Futoshiki
Sikaku
Tents Puzzle
Fillomino
Classic Word Search
Cryptogram
Cryptic Cross
Kendoku/KenKen
Slither Link
Gokigen
Roundabouts
Domino Puzzle
Word Crunch
Conceptis Daily/Weekly Puzzles

 

 

 

The Not So Famous Utilities Puzzle & Solution


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?

Most common solution or should I say No Solution. 
Diagrams Are Below....

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.

 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
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
(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
Go to this website and scroll down:
 It looks like "Eight Is Enough."
 Bari Graves
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

They answer is, you have to see things in a three dimensional kind of way, you
have to roll the piece of paper, which will enable you to re-route all three
gas, electric and water to each house, without having any of the lines touch
or cross each other

 

We did the "three houses, three utilities" question last year in
Math's class, and it has been proved to be impossible on a 2-D
representation due to the fact that there is an odd number of lines,
etc... If I had my math's book here I could explain it, but trust me -
it is impossible unless you made the representation 3-D, which is not
the question! Hopefully someone who has their math's book or similar
can explain the theory behind the question! ;-)
Hope I helped,
Jessi

Other variations

Align 3 triangles over 3 circles.
Connect each of the triangle to each of the circles.
Do not cross any lines.
Do not fold the paper.
Stay on one side of the paper.
Do not intersect any of the circles.
Do not rearrange the shapes.
You have 3 squares and 3 circles and you have to drawn a line from each circle to each square without overlapping them and you cant put the squares in the circles or the circles in the squares please help me thank you 
Crossword
Today's Brain Teaser Today's Trivia
One morning a man is leaving on business trip and finds he left some paperwork at his office. He runs into his office to get it and the night watchman stops him and says, "Sir, don't get on the plane. I had a dream last night that the plane would crash and everyone would die!" The man takes his word and cancels his trip. Sure enough the plane crashes and everyone dies. The next morning the man gives the watchman a $1,000 reward for saving his life and then fires him. Why did he fire the watchman that saved his life?
Solution
Which country has governed Greenland since the 14th century?

1. Norway
2. Iceland
3. Canada
4. Denmark
Solution
I Find It Interesting Featured Game
Tidy Guidelines For Enjoying Games
Video games can be a warm commodity. Game titles have swept the planet and might be played on numerous devices, for example TVs, computers or cell phones. In order to game with everyone, adhere to along and look at this short article to obtain your online video game playing knowledge up-to-velocity. Look for a number of retailers just before buying a online game. Make sure you appearance both on the web and in real traditional stores in the area. The cost of a youtube video game can differ commonly....
Read On
| All Our Fun Articles
It's time to play the Family Feud (TM) - the fast-paced game based on the successful TV game show. Two games for one low price! Try to guess what 100 people said when they answered our survey questions. Beat the average score -- or go head-to-head with a friend or an entire family! Pass, Play, Steal and Strike. Hours of fun with over 2,000 questions and 10,000 answers in each game! Survey says: Let's play Family Feud (TM)! Free Download
Take A Look Weekly Puzzles & Archives

WEEKLY PUZZLES: Pyramid Word Puzzle, Word Scramble, Word Jumble, Quiz Wordsearch, Supreme Hangman, Secret WordJumbo Sudoku1 Minute Search and Sudoku, Fill In The Blanks, 5:00 Minute Word Search, Classic Fill In Puzzle, Bits N Pieces, Pick and ChooseNumbers Search, Math Crossword, Roman Crossword, Roman Number Search 
PUZZLE ARCHIVES:
60 Visual Brain Teasers | 356 Themed Crossword Puzzles | 223 ScrabbleCross Puzzles | 275 Themed Word Search Puzzles | 101 Word Jumble Sudoku Puzzles | 50 Word Square Puzzles | 142 Quick Word Jumble Puzzles | 97 Anagram Crosswords | 33 Word Jumble Quotes

Play Our Free Exclusive Daily Puzzles - View All Puzzles
Play Our Free Classic Retro Games - View All Games

 

Our FREE Ezines
View All

A Fun Zone Daily
Daily Brain Teaser
Daily Trivia Ezine
Puzzle Ezine
Daily Free Game
I Find It Interesting

Add Your Button Here

Bookmark and Share

Amazon And Your Done
Food
CandySlingo KindleBooksDVD
HobbiesMP3Music
SoftwareGift Cards
ToysMagazinesTV
Gold BoxInstant Video

 


ANY USE OF THIS SITE IS SUBJECT TO THE TERMS AND CONDITIONS OF USE AND PRIVACY POLICY OF afunzone.com
All Games and Puzzles on A Fun Zone are copyrighted or trademarked by their respective owners or authors.
Copyright 2014 A Fun Zone. All Rights Reserve