The Wednesday Morning Math Challenge: Week 14

Welcome to Week 14 of the Wednesday Morning Math Challenge. You can find solutions to the Week 13 puzzles here, along with — more importantly — discussions of some ways to approach them. Remember that the real goal here is to think creatively.

This week we’re going to play around with a fun mathematical structure that you may have seen before: Magic squares.

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A magic square is a square grid with n rows and n columns, filled with distinct numbers from 1 to n^2, such that the sum of the numbers in each row, column, and both long diagonals is the same.

1. Can you come up with a 2×2 magic square?

2. What about a 3×3 magic square?

3. What value does each row, column, and long diagonal need to sum to in a nxn magic square?