# LR Visualisation: Cube Puzzle

You are here: Home  CAT Questionbank   LR Math Puzzles  Cube Puzzle Q.2

## LR Visualisation Puzzle: Cube

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.

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

512

## Detailed Solution

General Solution

The first layer of the cube looks like this:

We notice that each of the cubes in the second layer will be 64 + n, where n is the small cube directly below the cube in question. Each of the cubes in the third layer will be 64 x 2 + n, and so on.

In general, to find the number on a particular cube 'P' on the k'th layer, we can use the formula P = (k - 1)x64 + n, where n is the number on the bottom-most cube below P. With this general idea, we can solve the whole puzzle.

Solution for Question 2
The body diagonal that has the cube numbered 1 starts in the bottom-left-front corner and extends all the way to the top-right-back corner. This cube will have the number ${P=(8-1) \times 64 + 64=512 }$

Basically this is the last cube that is placed.

## Our Online Course, Now on Google Playstore!

### Fully Functional Course on Mobile

All features of the online course, including the classes, discussion board, quizes and more, on a mobile platform.

### Cache Content for Offline Viewing

Download videos onto your mobile so you can learn on the fly, even when the network gets choppy!