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

Puzzles and Curious Problems by Henry Ernest Dudeney: $291$

Progressive Squares

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

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.

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Magic Square, Measuring, Weighing, and Packing Problems: $291$. -- Progressive Squares
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Combinatorial & Topological Problems: Magic Square Puzzles: $391$. Progressive Squares