Explanation

The 35x35 magic square is similar to the 15x15 and 21x21 magic square, but there is a slight difference. You can composite the 15x15 and 21x21 magic square by using a 3x3 and 5x5 respectively a 3x3 and 7x7 magic square. You can composite the 35x35 magic square by using a 5x5 and 7x7 magic square. If you use a panmagic (and symmetric) 5x5 and a panmagic (and symmetric) 7x7 magic square, than you can composite a 35x35 magic square which is panmagic (and symmetric).

Construction methods

See for all possible construction methods the 15x15 or the 21x21 magic square.

See below the composite 35x35 magic square which is constructed by using an ultra magic 5x5 square and an ultra magic 7x7 square (= composite 1 up to 3), a composite 35x35 magic square consisting of 7x7 proportional 5x5 panmagic squares (= composite 4), a composite magic square consisting of 5x5 proportional 7x7 panmagic squares (= composite 5)  en an ultramagic 35x35 square which is constructed by using a 5x7 =7x5 magic rectangle.

• Composite 35x35 (1)
• Composite 35x35 (2)
• Composite 35x35 (3)
• Composite 35x35 (4)
• Composite 35x35 (5)
• Ultra magic 35x35

Use composite 35x35 (1) and (2) to construct a symmetric and panmagic 35x35 square.

Use composite 35x35 (3) to construct a symmetric, 5x7 and 7x5 compact and panmagic 35x35 square.

Use composite 35x35 (4) to construct a 5x5 compact and panmagic 35x35 square and each 1/7 row/column/diagonal gives 1/7 of the magic sum.

Use composite 35x35 (5) to construct a 7x7 compact and panmagic 35x35 square and each 1/5 row/column/diagonal gives 1/5 of the magic sum.

The ultramagic square is symmetric, panmagic and 5x5 & 7x7 compact.