Half Done
Eketahuna had a job to do.He was to paint a square floor that measured 144 feet on each side.When he saw the room,he knew that he didn't have enough paint for the job but he did what he could.At the end of the day,half the area of the floor was painted but when he measured the unpainted part,it was still 144 feet from top to bottom and 144 feet from side to side.
How is this possible?
How is this possible?
posted by Knightmare at
8:23 PM
27 Comments:
you know how those painters are! he was had been clouding his judgement all day long with a bottle of vino ... and upon measuring at day's end, he measured the same dimension twice :)
or ... he painted half the floor in the very center ... and therefore when he measured the unpainted area, it would measure 144' x 144'.
I think the floor he was painting needed to be checkered. And he only had one color of paint.
no winners yet
he was painting one surface of a cube ... when half was finished, one unpainted dimension would be 144'. Then it was stated that he measured from top to bottom ... on the cube, still 144' (kind of a stretch :))
or ... :)... he was using paint which dried invisible ... thus the unpainted floor would still appear to be 144' x 144'
I can't quite decide if the comment "top to bottom" means anything special ...
or ... :) ... maybe he was painting in the 4th dimension ... can't quite visualize that, but it sounds cool
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Zaux...you're thinking too much!
or ... :) ... he was painting the floor of a moving sidewalk and when he gave out of paint, the part he already painted had moved out of the 144' x 144' area ...
jeez! Knightmare .. running out of ideas
Zaux, the 4th dimension is actually time, so it's physically the same to paint in the 3rd dimension and 4th.
On to the question... the floor had 2 faces, meaning like a sheet of paper that measured 144 feet on each side. He only painted 1 face, leaving the other face, which is 144^2 feet in size.
the diagonal of the square is between painted and unpainted area :)
kapakoi
he might have painted in the manner as if drawing chess-board and instead of white boxes of chess he left the floor unpainted and for black boxes he used the paint he had.
this way half of the floor will be painted, you can still measure it 144 on both sides in peices though and plus it will look good too
I reckon that kapakoi has a valid answer. Instead, he might have painted a square of sides just shy of 102 feet. He may have done that in one corner, leaving an L-shape or away from the edges leaving an unpainted border. I prefer the last option.
It is easier to see this one half and another, if the border runs on the diagonal of the square.
I reckon he painted a square 101.8 x 101.8 feet inside the larger square floor, leaving an approx 21.1 feet border unpainted on each side. This way the painted area is half of the total area, and the unpainted outer edge still measures 144 feet on each side.
Hi C ...
I knew that ... I slapped myself when I read your comment :)
after reading all the posts, I like 2 answers:
* my answer, that the center area was painted leaving the outer edges bare, which still measure 144' x 144'
and
* kapakoi's answer, that the line dividing the painted and unpainted is the diagonal, still leaving a 144' x 144' unpainted dimension
Hmmm, I hate painting, so suspect I painted a square in the top right corner, leaving an L shape left to do ... as per Chris. Top of L to bottom is 144, side to side of 144.
Ooops. I just noticed that Zaux had done the middle square idea first.
Probably wron g too, but: he had painted the four corners (4 * 45° triangles) leaving a 101.8 foot (approx) sided diamond unpainted. The diagonal lengths are 144 feet.
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probably not wrong Chris...that's right
source answer:he painted the 4 corners leaving a diamond unpainted that's 144 feet top to bottom and side to side
you win the other half of the job
Cgris ...
I like you last idea
Hi Zaux. You were right to be suspicious about the "top to bottom" phrase.
painted diagonally.....
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