**Tags:** linear_algebra

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The challenge provides us with an image that has 26 words paired with numbers. Think of each word as an equation, and all words together as a system of linear equations.

For example, the first pair is apple 453. This can be thought of as a + 2p + l + e = 453.

Each equation has infinite solutions, but together as a system they have 1 solutution. In the solution, a = 70, b = 35, etc. If you put them in alphabetical order, they will be the ascii values for the flag.

Use any tool to solve this. I chose to represent the systems of equations as sage matricies and have sage do some linear algebra to solve them.