# Solution to The Light World

### by Oliver Kosut and Andrew Thomas

Given are three views of a 3x3x3 cube in which each box contains either a "smoke", or a mirror. The color shown at a given patch is the color that would come out of that patch if white light were shown into the appropriate patch somewhere else on the cube (equivalently, it is the color that would come out of another patch if white light were shown into this patch). The numbers shown when the cursor hovers over a square is simply a more precise value for the RGB color values than is available from the 24 bit color encoded by the HTML.

Each mirror is oriented so as to affect two of the three dimensions; light passing orthogonal to a mirror flows through it without being affected. The smokes are filters; they have RGB values that are n/26 for some integer n between 1 and 25. When light passes through a filter, each channel is multiplied by the corresponding channel of the filter. Thus each number as seen on the outside of the cube is a multiple of 1/26^k where k is the number of filters that the light has passed through.

The first step is to solve the logic puzzle to determine what is in each box in the cube. The solution is as follows. Trapezoids indicate mirrors with the long side closer to the top of the cube.

Top slice:
 7183 91715 191717 11717

Middle slice:
 16122 14141 51520

Bottom slice:
 181217 15117 15171 19179

To get the three answers, look at the smokes as viewed from each of the three given angles, and convert numbers to letters for the channel indicated by the color of the label in the puzzle. For example, Top is labeled red, so look at the red channel values of the filters. Order them left-to-right top-to-bottom as seen from the top. This does not impose a complete ordering, because in two shafts, there are two filters rather than one, but it can be easily determined which order the two filters should come in. Doing this gives the answer PROGINOSKES. For the other two angles, the answers are shorter than the number of filters, so ignore 17s, which act as padding, to get GRANOLA from the front and OCTAVIA from the right.