[superprismatic]

A message is written in the cells of

a rectangle having six rows and eight

columns. A piece of cardboard with

twelve holes cut out is placed over

this and the twelve letters exposed

read off. The cardboard is given a

180 degree turn and the next twelve

letters read off. At this point the

cardboard is turned over around the

vertical axis and twelve more letters

are read off. A final turn of 180

degrees allows the last 12 letters to

be read off. The result is: UNOLU

WUPNU ELGDH RDGHW EDEOL HTELH

TYEYP NAAWA SIOAO WAE. Read the

message.

SUPERPRISMATIC CLARIFICATIONS:

(1) The message is written in by rows,

left-to-right and top row to bottom

row.

(2) The sets of twelve are read off

left-to-right and top-to-bottom.

(3) The cryptogram is written in

groups of five for easy reading.

The spaces are irrelevant.

(4) Remember that the cutouts must

be designed so that any letter is

exposed in one, and only one, of the

four orientations of the piece of

cardboard

(5) It might be instructive to

design such a scheme yourself out of

graph paper to see how to make good

cutouts and to see how letters are

scrambled by it.

[Guest]

i need the answer!

[Guest]

It seems that either I am missing something or there is some information missing in the question

Given the question as is and my understanding of it, there are many ways to make such 12 cuts on the cardboard.

Consider the 6x8 rect as divided into 4 quadrants. Make any number of cuts on the top left quadrant and the ramaining on any other quadrant such that they are not mirror images of cuts on the first quadrant.

After the 4 rotations, all characters will have been seen (only once). example a cut made on the top left character would after 4 rotations as suggested in the question would cover top right, bottom right and bottom left cells.

Explanation:

Consider the 6x8 rectangle as below and the cardboard will cuts for all 12 characters in the first quadrant:

Now the 4 rotations are as below:

So, you can see all 48 characters once in 4 rotations.

Now, the same would apply even if you cut any other quadrant or for that matter, making cuts that are not mirror images of cuts made on the first quadrant. For example:

[superprismatic]

It seems that either I am missing something or there is some information missing in the question

Given the question as is and my understanding of it, there are many ways to make such 12 cuts on the cardboard.

Consider the 6x8 rect as divided into 4 quadrants. Make any number of cuts on the top left quadrant and the ramaining on any other quadrant such that they are not mirror images of cuts on the first quadrant.

After the 4 rotations, all characters will have been seen (only once). example a cut made on the top left character would after 4 rotations as suggested in the question would cover top right, bottom right and bottom left cells.

Explanation:

Consider the 6x8 rectangle as below and the cardboard will cuts for all 12 characters in the first quadrant:

Now the 4 rotations are as below:

So, you can see all 48 characters once in 4 rotations.

Now, the same would apply even if you cut any other quadrant or for that matter, making cuts that are not mirror images of cuts made on the first quadrant. For example:

Yes, there are many ways to make the cutouts. But, there is only one which will allow you to make a good English sentence. You are not asked to find the cutout pattern -- just find the sentence. Of course, once you get the sentence it is easy to reconstruct the pattern. There is enough information here to solve the problem.

[Guest]

I started by figuring the most likely letters to begin a word and worked from there. Once the first word was figured, well the saying became quite clear.

Laugh and the world laughs with you Weep and you weep alone

[bushindo]

I started by figuring the most likely letters to begin a word and worked from there. Once the first word was figured, well the saying became quite clear.

Laugh and the world laughs with you Weep and you weep alone

The brute force method is conceptually clear, but is a devil to program...

The full quote can be exhaustively searched in 4¹² searches. However, if we only want the top row and bottom row in plain text, we only need to search a 4⁴= 256 space, since the cardboard must include 4 and only 4 holes in the top and bottom row. Because of the rotation and reflection, to specify all possible configuration we only need to list 4 holes. Each hole can either occur in one of four quadrants, giving the space 4⁴ states. The reconstruction of the plain text, given a 4-length vector of holes-configuration is a devil to program. Once we construct a set of all 256 possible top-bottom row of plain text, this is the only one that stands out

[1] "LAUGHAND"

[1] "EEPALONE"

Of course, once we have the top row and the bottom row, we can apply the same method and get 256 possible combination of row 2 and row 5. However, the existing plaintext is a great help, and makes finishing a lot easier.

Edited August 24, 2009 by bushindo