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Logical Reasoning: VISUALISATION PUZZLE: CUBE

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Visualization Puzzle

A large cube, of total volume 512 cm3 is made up of smaller 1 cm3 cubes. The larger cube is made by following these rules:
1. Start from the left hand side, and number the small cubes 1 to 8, from left to right.
2. Place cube no. 9 behind cube no. 1 to start the second row, and proceed all the way to cube no. 64
3. Start the second layer on top of cube no 1, and build the second layer from left to right, and front to back like the first layer.

  1. On the bottom-most square layer of the cube, consider the surface diagonal that has the square numbered 8, find the sum of all the numbers on the cubes on this surface diagonal on the bottom-most layer.

  2. Find the number on the small cube at the other end of the body diagonal that has the small cube numbered 1.

  3. Find the number on the small cube at the other end of the body diagonal that has the small cube numbered 57.

  4. Find the sum of all the numbers on the body diagonal that has the small cube numbered 1.

  5. On the big cube, there exists an external surface whose four corner cubes have the numbers 8, 64, 449 and 512. Find the sum of all the numbers on the cubes on this surface.