## Trick for computing mod 13

Posted by mathfail
on March 24, 2011

- 0. Take any non-negative integer in base 10; for example, 4523.
- 1. Start at the most significant digit; in our example 4.
- 2. Now follow the hollow arrow once; i.e., we go to 1.
- 3. Now follow the solid arrows as many times as the next most significant digit; i.e., we follow the solid arrows 5 times to get 6.
- 4. Repeat steps 2-4 until you are at the least significant digit; i.e., we follow the hollow arrow to 8, then the solid arrows 2 times to 10, the hollow arrow to 9, and finally the solid arrows 3 times to 12.
- 5. Whatever number you end up at is your original number mod 13.
- 6. Memorize the graph to impress your friends.
- 7. Now figure out how to make your own for different bases and modulo different numbers.

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Impressive, if you don’t know Deterministic Finite Automata (DFA).

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