We say that an n x n square is regular provided that: It is a filled...

  

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We say that an n x n square is regular provided that: It is a filled square with numbers from 0 to n - 1. Having been expressed in base-n form, each base-n digit occurs exactly once in the n's position and exactly once in the units' position. (Also include the original magic square into the Excel table for justification.) 3 18 10 01 22 Example: 7 50 is regular since it is expressed in base 3 as 2 6 4 21 12 00 02 20 11 Construct an example of a 5 5 regular square. (Express your answer in both decimal and base-5 notation.) Is your square magic? a. Prove: Prove that every regular square is magic. b. Prove: Prove that the converse is not true by giving an example of a 4 x 4 filled magic square which is not regular. Your square should use integers from 0 to 15. Remember to give the magic sum and justify that your square is not regular. (Also include original magic square into the Excel table for justification.) We say that an n x n square is regular provided that: It is a filled square with numbers from 0 to n - 1. Having been expressed in base-n form, each base-n digit occurs exactly once in the n's position and exactly once in the units' position. (Also include the original magic square into the Excel table for justification.) 3 18 10 01 22 Example: 7 50 is regular since it is expressed in base 3 as 2 6 4 21 12 00 02 20 11 Construct an example of a 5 5 regular square. (Express your answer in both decimal and base-5 notation.) Is your square magic? a. Prove: Prove that every regular square is magic. b. Prove: Prove that the converse is not true by giving an example of a 4 x 4 filled magic square which is not regular. Your square should use integers from 0 to 15. Remember to give the magic sum and justify that your square is not regular. (Also include original magic square into the Excel table for justification.)