Sunday, February 21, 2010

Four sheep

Farmer Giles has four sheep. One day, he notices that they are standing in such a way that they are all the same distance away from each other. How can this be so?

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13 Comments:

Blogger Zaux said...

.....S....
.....H....
.....E....
.....E....
SHEEPEESH
.....E....
.....E....
.....H....
.....S....

Probably wrong, but the sheep stand as depicted with noses together.

February 21, 2010 3:54 PM  
Anonymous Simon H said...

Think in 3 dimensions! For 4 sheep to be equidistant they must be arranged in a tetrahedron, so I think one sheep is standing on a hill and the other three are arranged in an equilateral triangle around the base of the hill. Now.. GET ORRFF MOI LAAAND!

February 21, 2010 5:20 PM  
Blogger Chris said...

I'd love to say that Zaux has it by a nose, but I can't :( Simon H has got the correct answer :)

February 21, 2010 5:28 PM  
Blogger Zaux said...

good job Simon ...can't believe I didn't think 3-D

February 21, 2010 6:34 PM  
Blogger Ross said...

I like the by a nose answer better ... much more ToM :-)

February 21, 2010 7:17 PM  
Anonymous Anonymous said...

One of your sheep is spelled wrong zaux

February 21, 2010 7:33 PM  
Blogger Zaux said...

wrong spelling? ... I know ... typo ... sometimes, I'm a typing wizard

February 22, 2010 4:44 AM  
Blogger DualAspect said...

Maybe that one's dyslexic!

February 22, 2010 5:33 AM  
Anonymous Anonymous said...

there standing in the shape of a square

February 22, 2010 10:32 AM  
Blogger Chris said...

Hi Anonymous. Then the ones on opposite sides of the square are further apart than the ones next to each other.

If the sheep are all facing the same way and are identical, the tetrahedron arrangement makes every part of each sheep be the same distance to the corresponding part on the other three sheep.

February 22, 2010 1:50 PM  
Blogger Ross said...

So why doesn't the nose-in answer work? Assuming the noses are pointy and all four touch in a single point, the sheep are all at zero inches from each other. Is it just disqualified as an answer because their other parts end up forming a square and hence are not all equidistant?

February 24, 2010 1:50 PM  
Blogger Chris said...

Hi Ross. Opposite sheep are further apart than adjacent sheep. I'll accept, but only just, that their noses are equally far apart.

February 25, 2010 10:53 AM  
Blogger Chris said...

Hi Ross, you have given the reason for rejecting the "+" arrangement.

The tetrahedron is obviously better than the "+" or the "□" arrangement.

February 25, 2010 10:57 AM  

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