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This puzzle is based on NeedAName's recent puzzle, Determinant of Word Matrix.

The challenge:

Create a $3\times3$ matrix of distinct letters (i.e. no repeated letters) with no vowels in the middle row such that the six terms generated when calculating the determinant form valid English words.

Words are considered valid if and only if they are English words found on Dictionary.com (not including (pre/suf)fixes, abbreviations, acronyms, proper names, etc.).

For example, with a simple $2\times2$ matrix $\begin{bmatrix}O & I\\N & R\end{bmatrix}$, the determinant is $OR-IN$.
This forms two 2-letter words.

With a $3\times3$ matrix $\begin{bmatrix} A & B & C\\D & E & F\\G & H & I \end{bmatrix}$ you will end up with six 3-letter words:

$AEI + BFG + CDH -CEG - BDI - AFH$.

Since the actual determinant doesn't matter, the easiest way to think of this is as a $3\times5$ matrix with the first two columns repeated:

$\begin{bmatrix} A & B & C & A & B\\D & E & F & D & E\\G & H & I & G & H \end{bmatrix}$

Then you just need to make sure all the intact diagonals $\searrow$ and $\swarrow$ are valid words.

(For more information on finding determinants, see here or here)

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    $\begingroup$ +1 for superior formatting! I should have you organize my puzzles before posting them :) $\endgroup$
    – NeedAName
    Sep 22, 2015 at 17:47
  • $\begingroup$ Haven't you over-complicated the puzzle? The last para is enough to understand the question by itself. $\endgroup$
    – ghosts_in_the_code
    Sep 22, 2015 at 18:10
  • $\begingroup$ @ghosts I considered that, but it just seems really arbitrary to ask for a $3\times5$ matrix with certain repeated columns that fits a certain pattern. I thought keeping the determinant explanation in there would help people understand where the idea came from, so it's not quite so arbitrary. $\endgroup$
    – GentlePurpleRain
    Sep 22, 2015 at 18:56

1 Answer 1

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With the help of a list of three-letter words and an automated search:

$\begin{bmatrix} A & I & O\\F & D & C\\E & T & S \end{bmatrix}$ producing the words ADS, ACT, IFS, ICE, OFT, and ODE.

Here are all 50 results my program found.

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  • $\begingroup$ Could you elaborate on how you found this, or did you just brute force it? $\endgroup$
    – user1717828
    Sep 22, 2015 at 18:01
  • $\begingroup$ I suppose I should have added a no-computers tag (since that was my intention), but kudos for finding 50 different solutions! $\endgroup$
    – GentlePurpleRain
    Sep 22, 2015 at 18:57

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