# Answer to Question #6617 in Abstract Algebra for prince

Question #6617

An ant lives on the surface of a cube with edges of length 7cm. It is currently

located on an edge x cm which is 2cm from one of its ends. While traveling on the surface of the cube,

it has to reach the grain located on the opposite edge (also at a distance xcm which is also equal to 2 cm from one

of its ends)

(i) What is the length of the shortest route to the grain if x = 2cm? How many routes of

this length are there?

(ii) Find an x for which there are four distinct shortest length routes to the grain.

located on an edge x cm which is 2cm from one of its ends. While traveling on the surface of the cube,

it has to reach the grain located on the opposite edge (also at a distance xcm which is also equal to 2 cm from one

of its ends)

(i) What is the length of the shortest route to the grain if x = 2cm? How many routes of

this length are there?

(ii) Find an x for which there are four distinct shortest length routes to the grain.

Expert's answer

(I) The shortest way is 2+7+7+2 = 18 sm. There are 2 such ways.

(II) For x=3.5 sm (middle of the edge) there are 4 such ways.

(II) For x=3.5 sm (middle of the edge) there are 4 such ways.

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