# Diagonalization

Diagonalization is a common positional extraction method used in hunt puzzles. It involves lining up a series of strings and reading the letters on one of the diagonals to get a new string.

## Puzzle Application

As with most other positional extraction methods, diagonalization is almost exactly what it says on the can: reading the letters along the diagonal of a series of answers. Functionally, this means that one would read the first letter of the first answer, the second of the second answer, etc. Identifying which answer is "first", "second", and so on will often require a reordering mechanism.

Diagonalization is best applied to a series of answers that are all the same length, in addition to that length being the same as the number of answers in the series. This allows for the extraction line to be a "true" diagonal, travelling from corner to corner. While not a strict rule, this practice has become commonplace to provide the cleanest solve path.

While it is most common for diagonalization to go from the upper-left corner to the lower-right corner, it's possible for the extraction to use the lower-left to upper-right diagonal instead, or have the answer read in the opposite direction for either of these lines. However, all of these alternate methods are less common and are more likely to be missed by solvers.

Diagonalization also doesn't necessarily need to be applied to a series of standalone strings. It can be applied to any square grid of characters, such as crosswords, certain logic puzzles, or a long string of text that has a square number of characters (and therefore can be rearranged into a square). It can also be applied to a series of sentences, where (instead of first letter of first word, etc.) one takes the first word of the first sentence, the second word of the second sentence, and so on, to form a new sentence.

While relatively simple in execution, diagonalization can easily be abused if not properly clued. If one of the variations are used, particularly where text is going backwards along a diagonal, there should either be a clue to that extraction somewhere else in the puzzles (flavortext, explicit mid-puzzle instruction, etc.), or it should be an intuitive step in the process (e.g., if the puzzle is about extracting words using that method, it would be an expected final step via recursion).

## Strategy

### Identification

As mentioned earlier, diagonalization is best used with squares, so if one is left with a square of characters and no clear way to extract, it would be wise to check the diagonals. Even if a set of answers does not form a perfect square, it's still wise to read the diagonals to see if they form anything useful. Diagonalization is an extraction method that is relatively robust against tools like anagram solvers, as it is unknown which letters are to be extracted until the order of the answers is deduced. Therefore, it can be a natural fit for puzzles that have their reordering step comprise a large bulk of the puzzle.

Even if there is no exact indication that diagonalization is needed, it may be worth quickly checking anyways. Sometimes things are just underclued, and there's nothing you can do but go through your options!

### Extraction

On the other side, if one believes that diagonalization is the correct extraction method but the usual upper-left-to-lower-right diagonal isn't providing anything useful, there are two steps that should be taken before giving up.

1. Check to see if the other diagonals provide anything of use. They may not have been clued as strongly, but if you believe that diagonalization is correct, it's worth pursuing.
2. Make sure that your text is ordered correctly AND entered correctly. If a series of answers are in the wrong order, none of the diagonals will work. Similarly, if a crossword is incorrectly filled, a text wrap has been done in the wrong direction, or an answer has been misspelled, the resulting diagonals may be incorrect. Check your work and try Step 1 again.

## Notable Examples

• Be Noisy (MITMH 2002) (web) - An unintentional solution to the nonexistent "Hotels Metameta" that resulted from two teams taking the diagonal of the answers. This resulted in a 7-letter 'answer' from 8 feeders, as the last was too short to be extracted from.
• Epcot Center Meta (MITMH 2006) (web) - Click to revealContained fourteen 14-letter answers, which (when arranged properly), could read not only the phrase 'VANILLA CARIBOU' down the primary diagonal, but also 'STRAWBERRY DEER' up the opposing diagonal.