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# 4 matches, then 3

## Question

Arrange 4 matches into a square. You get 4 right angles.

Halve their pair wise separations (think tic- tac- toe) and you get 16 right angles,

Show how you can remove 1 match and form 12 right angles.

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a three dimentional figure, two matches makes a cross and the third one crosses them through the centre perpendicularly,in this case we will have 12 right angles

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maybe its not this simple?

hmmm.... pair wise seperations is not a term i understand and google did not
help! but if i understand this properly(and i wouldn't be surprised if i don't)
then you have 4 matches originally lets number them 1 through 4 starting with
the top of the square and working clockwise 2,3,4. then you are adding 2 more
matches? i'm thinking one down the centre of the square vertically and one
horizontally? then would you not just remove match number 2 and leave the sqaure
open to eliminate 4 of the angles? tell me if i'm way off on the meaning of the
question.

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1080 degrees= 12 right angles....

so we can make a triangle having three crossed sides and forming 12 angles having a total of 1080 degrees...so are equal to 12 right angles.
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Removing any one of the sides of the bigger square will leave us with 12 right angles and it will look like this:

----------------------- -----------------------
I I I I I

I I I I I
I I I => I I
I----------I------------I I-----------I-----------
I I I I I
I I I I I
----------------------- ------------------------

(I don't know whether you got what i meant because my so called picture looks terrible)

Edited by Krishna Kutty
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I see that i got the question wrong!

maybe its not this simple?

hmmm.... pair wise seperations is not a term i understand and google did not
help! but if i understand this properly(and i wouldn't be surprised if i don't)
then you have 4 matches originally lets number them 1 through 4 starting with
the top of the square and working clockwise 2,3,4. then you are adding 2 more
matches? i'm thinking one down the centre of the square vertically and one
horizontally? then would you not just remove match number 2 and leave the sqaure
open to eliminate 4 of the angles? tell me if i'm way off on the meaning of the
question.

See my spoiler and you can see what i thought would be pair wise separation!

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I meant to move the sides of the square closer to each other to get something like this: #

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1080 degrees= 12 right angles....so we can make a triangle having three crossed sides and forming 12 angles having a total of 1080 degrees...so are equal to 12 right angles.

Actually each of 12 angles is a right angle.

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a three dimentional figure, two matches makes a cross and the third one crosses them through the centre perpendicularly,in this case we will have 12 right angles

do you mean like 8 + 4 right angle?

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a three dimentional figure, two matches makes a cross and the third one crosses them through the centre perpendicularly,in this case we will have 12 right angles

do you mean like 8 + 4 right angle?

coordinate axes for x y z.

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