CISRA Puzzle Competition 2008 - Solutions

This is the archive of the 2008 Puzzle Competition. Please visit the current competition site for information about the latest Puzzle Competition.

C.3 Through the Looking-Glass

The first thing to notice about this puzzle is that the cubes in the image are not distributed arbitrarily through the 3D space. Each cube sits at a discrete height above the floor, marked by the number of bulges on the rod supporting it, which varies from 1 to 5. Each cube also sits in a discrete position within the grid of squares on the floor. The square tiles are three times as long and wide as a cube, and the cubes sit above one of the nine positions within a 3×3 grid in each square.

In other words, each cube is a voxel, sitting at one of five different heights when looked at side-on, and fitting into a grid when looked at from above (with each floor tile corresponding to 3×3 grid squares).

You can also determine by examining the image that exactly one cube occupies each of the grid positions running from left to right (i.e. exactly three cubes per column of square floor tiles).

These constraints are enough to allow working out the 3D coordinates of each cube, resolving all of the ambiguities which occur where cubes or rods are hidden behind each other, or where the shadows and focus blur interfere.

This set of 3D coordinates can be represented as shown by the first hint for this puzzle:

In this image, the cubes are plotted as they would appear from above, with the heights written on each green square. To solve the puzzle, you need to work out how the structure would appear if you looked at it side-on from the right, ignoring perspective distortion. Equivalently, you could imagine what the shadow on the left wall would look like if you put a distant light source opposite it on the right.

To transform this diagram into the equivalent view from the right side, you can throw away the horizontal position, and fill in a square grid using the depth and height coordinates of each cube. You end up with a grid that looks something like this:

...which spells out the answer: BANJO.