Silverfish and the Rubik's cube
Remember the bookworm Silverfish
This time he finds a Rubik's cube made of wood. He starts at the center of face of any one of the outside cubes and bore a path that takes him once through every cube. His movement is always parallel to a side of the large cube, never diagonal.
Is it possible for the Silverfish to bore through each of the Rubik's side cubes once and only once and finish his trip by entering the final central cube for the first time?
This time he finds a Rubik's cube made of wood. He starts at the center of face of any one of the outside cubes and bore a path that takes him once through every cube. His movement is always parallel to a side of the large cube, never diagonal.
Is it possible for the Silverfish to bore through each of the Rubik's side cubes once and only once and finish his trip by entering the final central cube for the first time?
Labels: friday special, logic, puzzle, thinktank
posted by Rajesh Lal at
5:25 PM
9 Comments:
depends, What size is the cube? 2x2, 3x3, 4x4 etc...
wait... i got the first post?!
It's obviously a 3x3x3 cube, otherwise there wounldn't be one central cube. No, it's not possible.
It's simply impossible because of the quantium phsics.
OBVIOUSLY
It's simply impossible because of the quantium phsics.
OBVIOUSLY
Its definitly possible, so long as he can make a 90 angle turn in one cube... cus its not going diagonally, or going through that cube 2 times... hes entering on one side, and comig out an other!
i basicly drew a cube opened up, and drew a path... its pretty random, so i cant explain it, but you start in the center face of one side, end at the center of an other face, and then go in the middle cube.
and annonymous #1: its a rubix cube, so its a 3x3 cube...
No, it is impossible.
To prove, let us take a the simplest rubik's cube with a central cube ... a 3x3x3 cube.
This proof can be extended to other cubes with a central cube .... odd x odd x odd cubes.
Let each of the 1x1x1 cubes forming the 3x3x3 rubik's cube be alternately colored
black and white (i.e. each cube adjacent to a white cube is black and vice versa).
If we make the 8 corners of the rubik's cube be black, the 1x1x1 cube forming
the center of each of the outer layers of the rubik's cube would be black.
The central cube of the rubik's cube would be white.
With this alternate color arrangement, there would be 13 white cubes and 14 black cubes,
the central cube being white.
As the silverfish bores the cubes in the direction that his always parallel to the side
of the Rubik's cube, it would in effect be boring each cube alternately black ...then white
,,, then black... then white ... etc.
As there are 14 black cubes and 13 white cubes, to bore each small cubes only once,
it should start boring with the black and ends with a black.
Thus, to finish by entering the central cube (which is white) for the first time, would be impossible..
Regards/Rudy
Yo, i can solve the stupid cube in under a minute ten! a 2x2 two in 30! a 4x4 in six! a 5x5 in 10! what the heck is the question! i don't understand! i can solve a 5x5 but i don't even understand a stupid logic question! someone help!
gifted but mentally challenged mr. anonymous.
sure let him start boring and if he gets stuck, stat "solving" the rubix cube so a new path opens up... assuming he can fit inside a cube.
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