Henry Ernest Dudeney/Puzzles and Curious Problems/291 - Progressive Squares

by : $291$

 * Progressive Squares
 * This is a magic square, adding up to $287$ in every row, every column, and each of the two diagonals.


 * Dudeney-Puzzles-and-Curious-Problems-291.png


 * If we remove the outer margin of numbers we have another square giving sums of $205$.
 * ''If we again remove the margin there is left a magic square adding up to $123$.


 * Now fill up the vacant spaces in the diagram with such numbers from $1$ to $81$ inclusive as have not already been given,
 * so that there shall be formed a magic square adding up to $369$ in each of twenty directions.