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An ant had to travel from one corner of a room to diagonally
opposite corner. It can walk on walls, floor and roof only.
How will you find the shortest path for this ant ?
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Answer Posted / kelley w.
The room is a rectangular prism (like a cube only
rectangular). The 4 floor corners will be represented by
A,B, C, and D. The ceiling corners will be represented by
E, F, G, and H, with E being directly above A, F being
directly above B, Gbeing directly above C, and H being
directly above D. (Draw a picture, it helps) the ant needs
to go from the floor corner A to the ceiling corner G (if
I’m not mistaken). The shortest path would be a diagonal
line from A to G, but seeing as the ant cannot walk on air,
we have to find the quickest path using the walls, floor
and ceiling.
F__________G
/| /|
/B|________/_|C
E/_________H/ /
| / | /
|/_________| /
A D
The ant has four logical choices:
1) He could cross diagonally from A to C, then crawl
up the wall to G. We would have to find the length of
diagonal AC and the height of the room, which would be CG.
(He could also crawl up from A to E, and then diagonally
from E to G, but this would be the same distance as the
aforementioned choice.)
2) He could cross along the wall from A to D, then
crawl diagonally up the wall from D to G. We would have to
find the width of the room, which would be AD, and the
length of diagonal DG.
(He could also go diagonally from A to F, and then crawl
along the ceiling from F to G, but that would be the same
distance as the aforementioned choice.)
3) He could cross along the floor from A to B, then
crawl diagonally from B to G. We would have to find the
length of the room, which would be AB, and the length of
diagonal BG.
(He could also go diagonally from A to H, and then crawl
along the ceiling from H to G, but that would be the same
distance as the aforementioned choice.)
4) He could cross along the wall from A to the
midpoint of DH, then continue from the midpoint of DH to G.
We’ll call the midpoint of DH “M”. We would have to find
the width of the room, which would be AD, and half the
height of the room, which would be DM and HM. We would then
have to find the length of the diagonal AM, and then the
length of the diagonal MG.
(He could also go diagonally from A to the midpoint of BF
and then diagonally to G, but this would be the same
distance as the aforementioned choice.)
Using common sense, we can see that choice 4 will be the
quickest route for the ant. If you have trouble seeing how
this option is quickest, make up fake dimensions for the
room and find the values I mentioned above for each choice
to determine the shortest distance.
(For example, pretend the room is 5 feet high, 10 feet
wide, and 20 long. AE=5, AD=10, and AB=20.)
| Is This Answer Correct ? | 43 Yes | 12 No |
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