7x a week
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
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.
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
= [n/2] [(n-1)/2] [m/2] [(m-1)/2] where [x] denotes the
integer part of x.
the minimum crossing number of Cr(3,3) = [1.5]  [1.5]
 = 1 * 1 * 1* 1 = 1.
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
(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. )
Go to this website and
It looks like
"Eight Is Enough."
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.
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
representation due to the fact that there is an odd number
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
can explain the theory behind the question! ;-)
Hope I helped,
|Align 3 triangles over 3
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
|Halloween was almost over, and Mr. Green had less than 20 candies left. When the doorbell rang, he thought he would give all the candies away. When he opened the door, there were two trick or treaters. He wanted to give away the candies evenly, but he noticed that when he divided the candies in two, there was one left over. At that point, he saw another trick or treater behind the first two. He tried to divide the candies evenly among the three of them, but again one was left over. Finally, another trick or treater came to his door, making it four trick or treaters altogether. Mr. Green still had one candy left over after dividing the left over candies in fours. How many candies did Mr. Green have left when the doorbell rang?
|Halloween is the second most commercially successful holiday, what is number 1?
4. Valentines Day
Find It Interesting
|The History Of Halloween Music
Some may debate whether Bobby Pickett’s “Monster Mash” or the beginning of Johann Sebastian Bach’s “Toccata and Fugue in D minor” was the first music to unequivocally be associated with Halloween, while other’s may insist that nothing truly scary made an impact on the national consciousness until the Starland Vocal Band released “Afternoon Delight”. No matter what you associate musically with Halloween, the songs...
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