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Sweet path

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post-53237-0-97331500-1390728467_thumb.j

An ant at A trails the shortest track from A to B
on the sugar cubes structure as shown. Then it
went through the shortest tunnel from B to A.
How far it travelled to B and back to A?

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Posted (edited) · Report post

This problem isn't presented clearly.

1) The shortest track from A to B

ON the sugar cubes might entail

going through the tunnel and ON

the sugar cubes.

2) "Through the shortest tunnel!?"

There is only one tunnel. That is, there

is only one hole.

If you mean going from A to B *without*

passing through the hole (and be the shortest route),

then you're going to have to state that.

And then if you mean the return trip from

B to A must pass through the hole (and be

the shortest route), then you are going to

have to state that as well.

An ant at A trails the shortest track from A to B

on the sugar cubes structure as shown. Then it

went through the shortest tunnel from B to A.

How far it travelled to B and back to A?

Edited by Perhaps check it again
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Posted · Report post

This problem isn't presented clearly.

1) The shortest track from A to B

ON the sugar cubes might entail

going through the tunnel and ON

the sugar cubes.

2) "Through the shortest tunnel!?"

There is only one tunnel. That is, there

is only one hole.

If you mean going from A to B *without*

passing through the hole (and be the shortest route),

then you're going to have to state that.

And then if you mean the return trip from

B to A must pass through the hole (and be

the shortest route), then you are going to

have to state that as well.

An ant at A trails the shortest track from A to B

on the sugar cubes structure as shown. Then it

went through the shortest tunnel from B to A.

How far it travelled to B and back to A?

there are 2 paths "on" surface and "through" tunnel.. the 2X1X1 hole is NOT the tunnel.

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Posted · Report post

Does "tunnel" mean the tiny gap between the cubes? From B, he still need to travel on a surface to get to a gap between 2 cubes. Is that acceptable?

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Posted · Report post

The shortest way from A to B is a bit more than 5,84 units (red line in the left picture).

From B to A the ant travels by the diagonal of an imaginary plane between lines ef and ab (folded a bit at the line cd) - yellow line in the right picture. Should be some 5,49 units or so. Maybe. :unsure:

post-52539-0-43583800-1390946290_thumb.j

Sorry for my English.

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Posted · Report post

i cant fully visualize this just yet but think the ant can travel ever so slightly shorter than kukupai's answer above

(34)

.5

EDIT:

post-17529-0-61951700-1391007980_thumb.j

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Posted (edited) · Report post

Well done kukupai & plainglazed...nice illustration!

Edited by TimeSpaceLightForce
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