Twelve colored cubes are arranged in a row. There are 3 blue cubes, 2 yellow cubes, 3 red cubes, and 4 green cubes, but not in that order. There is a yellow cube at one end and a red cube at the other end. The red cubes are all touching. The green cubes are also all touching. The tenth cube from the left is blue. What color is the sixth cube from the left

The sixth cube from the left is a green cube.

Step-by-step explanation:

There are 12 cubes, 3 blue cubes, 2 yellow cubes, 3 red cubes, and 4 green cubes.

Let B, Y, R and G represent blue, yellow, red and green cubes respectively.

The arrangement will be predicted with the information provided

- There is a yellow cube at one end and a red cube at the other end. There are two models to this.

Y, , , , , , , , , , , R

Or

R, , , , , , , , , , , Y

- The red cubes are all touching. Note that there are 3 red cubes

Y, , , , , , , , , R, R, R

Or

R, R, R, , , , , , , , , Y

- The green cubes are also all touching and the tenth cube from the left is blue.

We first position the blue cube at a position tenth from the left

Y, , , , , , , , , R, R, R

With this configuration, the blue cube will be taking the position of a red cube and that violates the rule that the 3 red ctubes are touching, Hence, it is evident that the 2nd model we're examining is the correct one

We then position the blue cube at a position tenth from the left in the 2nd model

R, R, R, , , , , , , B, , Y

Then all the 4 green cubes are touching, they could be placed in a number of ways

R, R, R, G, G, G, G, , , B, , Y

Or

R, R, R, , G, G, G, G, , B, , Y

Or

R, R, R, , , G, G, G, G, B, , Y

Note that in each of the 3 possible ways this can happen, the sixth cube from the left is always a green cube.

Hence, the sixth cube from the left is a green cube.

Hope this Helps!!!

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