Silverfish on Diet
Silverfish found a wooden cube this time*. He starts crawling from one corner of the cube, and, confining himself to its edges, which are all exactly one cm long, crawls as far as he can without retracting any part of his path.
How far does he crawls?
* Silverfish old adventure
How far does he crawls?
* Silverfish old adventure
Labels: mathemagic, trickofmind
posted by Rajesh Lal at
10:09 PM
17 Comments:
9 cm
I dont know the mathematical reasoning, but it worked out to be 9 in practice
Highest/Longest I got was 9cm.
I agree with Daniel.
~Cassieadams01
9 cm.
How long is the silverfish? did his head start at one corner? or tail, with his head somewhere already along the first route? If he's more than 1cm long, then did he start at one and already partly wrapped around to the next edge?
If the silverfish has a practile length of 0cm, or his head started at the corner with his tail wrapping to a different edge, then I agree with the above.. 9cm.
Otherwise, his length has to be taken into consideration.
of course, the other answer could be 1cm. because the cube is contained in an area of 1x1. so he's just crawling around the cube, but never gets more than 1cm awa from his starting point (in 2D). if considering 3D.. then 2*sqrt(2) is the furthest he can get away from his starting point (diagonal corners).
One other condition I thought of.. is he only restricted from edges he's already visted? how about corners that he's already crossed from a different direction. If he can't revisit a corner twice, then 7cm is the most linear distance.. (or still the 2*sqrt(2))..
ok.. i'm done..
I got 9cm
well i got two answers.. 9cm is when the silverfish can cross a corner twice.. while i got 8cm for him to reach back to his starting position...
9 cm
unless of course he can jump ;) in which case he wouldnt crawl lol
Euclid, I think your math is a little wrong regarding the max distance from his starting point. These are the actual max distances:
1cm for a 1-dimensional cube
sqrt(2)cm for a 2-dimensional cube
sqrt(3)cm for a 3-dimensional cube
excuse me, but how the heck can you get a 2-dimensional cube??
Simple... You just have to look at how a cube is defined. A 3-dimensional cube (as most are familiar with) is one that is defined as having equal thickness in each dimension, ie width, length and height for a 3D cube. As such a 2D cube is simply one that has an equal length and width, which is more commonly referred to as a square. I am however surprised that you were taken back by the notion of a 2D cube rather than a 1D cube. But the same rules apply. In the case of a 1D cube, it simply has a length, thus the 1 cm I stated earlier.
its impossible to know! it does not state how he went from corner to corner, or how many times he went to each one. so my my point is, he could have travled from 6cm, to an infant amount of miles!!! and by the way, im only 11 years old and got that!
and anonymous, a cube has 8 sides and is 3-d. show me a square shapp that's 2-d
square root of 3 cm
take once side and find the diagonal witch is a^2 + b^2 = c^2 so 1 + 1 = 2^.5
then take the diagonal, square root of 2, a side connecting the end point of the diagonal of the side to the end point of the diagonal of the cube. it would be 2 + 1 = 3^.5 so the answer would be square root of 3
that one guy is right there is no such thing as a 1d or 2d cube. or else ity would be called a square.
yha. square=1 or 2-d. cube holds volume and therefor is a 3-d object.
(and jeremy, i have no idea what u just said0
use pythagorean's theorem, you know A^2 + B^2 = C^2
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