Posted on 2 June 2015

## Puzzle

*This week's Student-authored Challenge will refine your skills in trans-dimensional reasoning:*

Laxly filch の反対は?

## Hint 1 |
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For the "trans-dimensional" part of the clue, what 3-dimensional shape is suggested by the 2-dimensional image? How many of its smaller parts would be visible?

## Hint 2 |
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Note that the adjacent squares at the edges and corners have exactly one letter. It might help to fill in the blank sides and then read the clue again.

## Solution |
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The grid on the board is a pattern for making a cube from a sheet of paper or other flat stiff material. The 26 different letters of the alphabet are written on different squares. The pattern needs to be folded at certain places to make the edges of the cube. You may notice that in the pattern, there are no places along those edges where there are letters in more than one adjacent square - where there is a letter in a square, the other squares touching along any of those edges are always blank. That observation hold true even after the pattern has been folded into the shape of a cube. The "trans-dimensional" part of the clue refers to looking at the cube as 3 x 3 x 3 smaller cubes.

Some people may not find it easy to mentally picture the cube. And if you try to rotate and roll the image, you may not be able to restore all the angles to right angles. So...

- Recreate the flattened cube pattern with the white letters in the correct position. It may help to include a few tabs to fasten the sides. Another option would be to stick the pattern on a 3 dimensional cube, such as a 3 x 3 x 3 Rubik's cube.
- Note that on a cube consisting of 3 x 3 x 3 smaller cubes, 26 of those smaller cubes would be visible. When the pattern is folded, exactly one letter of the alphabet falls onto each of those cubes. It may help to write the letters for each small cube in the blank squares of the pattern, as shown in yellow on the pattern to the right.
- Looking at the clue
*Laxly filch の反対は?*the Japanese part translates to "The opposite of?". We need to find the letters that are on the opposite side of the folded cube. For example, the letter on the cube opposite from the "L" cube is "U" and opposite from the "Y" cube is the cube with the letter "R" as shown to the right. Using that method to translate the LAXLY FILCH part of the clue and moving the space to the right one position results in Utsuro Bune (うつろ舟) which is a hollow or empty boat or ship.

The solution is stl.la/utsurobune.