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I apologize in advance if this is not specific enough, but I'm trying to wrap my head around the following:

Say I have a list of phrases in 2 languages, for example English and Armenian, and words are repeated throughout the phrases. I have a very simple example below:

great red square      -   Մեծ կարմիր քառակուսի
small red circle      -   փոքր կարմիր շրջանակը
great blue rectangle  -   Մեծ կապույտ ուղղանկյան

By looking which words occur in which spots I can figure out what each word means in the other language. What I struggle with is writing out the solution using a mathematical approach. My math has gotten rusty, but what came to mind is using matrices. How exactly I'm not sure, and I'm not sure what to look (google) for specifically.

If someone can point me in the right direction (how to write this out, or which specific math subject to study) I would be very grateful.

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    It's an interesting idea but depending on the language you have to account for inflection/declension (assuming the phrases are sentences). In a purely analytic language this approach might work but any morphology would likely render this impractical. I love the question though as it fuses my two passions! – 2017-01-25
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    I think puzzles like this appear in the [Linguistics Olypmiad](http://www.ioling.org/). More generally, try searching "linguistics," "computational linguistics," "machine translation," or "natural language processing." – 2017-01-25
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    @Jahambo99 Good point, trying this with German would become a lot more difficult. Let's just assume using this in situations where no morphology occurs, how would I approach this then? – 2017-01-25
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    @dean2020 Then you have the issue of creating algebraic representations of given words and how they interact with each other. If you want to solve a system of linear equations, you can use gaussian elimination to reduce a matrix etc. etc. But what arithmetic do you use to represent words? – 2017-01-25

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