Before proceeding further below are the basic formulas to check the sums of magic and bimagic squares

  • Magic Sum
  • Bimagic Sum

where n is the order the magic square.

Below are bimagic squares of orders 100, 110 and 121. Order 100 is with blcoks of order 10. Orders 110 and 121 are with blocks of orders 11.

This work is Aale de Winkel‘s contribution and is obtained as private communication.
Aale’s web-site and e-mail:
Magic Encyclopedia magic square, magic cube, magic tesseract, magic hypercube and e-mail: <aaledewinkel@magichypercubes.com>.

Also this work is based on two bimagic squares of orders 10 and 11 constructed by Fredrik Jansson in 2004. For details see the linik: http://www.multimagie.com/English/Bimagic10&11.htm

Still there is one more bimagic square of order 121 constructed by author, where blocks of order 11 are pandiagonal magic squares of equal sums.

Bimagic Squares of Orders 10 amd 11

Below are bimagic squares of order’s 10 and 11 due to Fredrik Jansson in 2004. For details see the linik: http://www.multimagie.com/English/Bimagic10&11.htm.

Bimagic Square of Order 100: Blocks of Order 10

Below is an excel sheet of bimagic square of order 100 constructed by Aale de Winkel based on bimagic squares of order 10 constructed by Fredrik Jansson. Blocks of order 11 are bimagic squares with different magic and bimagic sums. In this case, we have

S100×100:=500050; Sb121×121:= 3333833350.

  • Excel sheel of bimagic square of order 100

Bimagic Square of Order 110: Blocks of Order 11

Below is an excel sheet of bimagic square of order 110 constructed by Aale de Winkel based on bimagic squares of order 11 constructed by Fredrik Jansson. Blocks of order 11 are bimagic squares with different magic and bimagic sums. In this case, we have

S110×110:=665555; Sb110×110:= 5369032185.

  • Excel sheel of bimagic square of order 110

Bimagic Square of Order 121: Blocks of Order 11

Below is an excel sheet of bimagic square of order 121 constructed by Aale de Winkel based on bimagic squares of order 11 constructed by Fredrik Jansson. Blocks of order 11 are bimagic squares with different magic and bimagic sums. In this case, we have

S121×121:=885841; Sb121×121:= 8646694001.

  • Excel sheel of bimagic square of order 121

Bimagic Square of Order 121: Blocks of Order 11

In this case, we have

S121×121:=885841; Sb121×121:= 8646694001,

Blocks of order 11 are pandiagonal and of equal sums, S11×11 :=80531. The magic squares of order 121 is also pandiagonal. See below an excel sheet for the order 121.

Excel sheel of bimagic square of order 121

The different between two bimagic squares of order 121 is that one is based on different magic and bimagic sums of order 11. The second is based on pandiagonal equal sums magic squares of order 11.

References

  1. Inder J. Taneja, Block-Wise Construction of Bimagic Squares: Multiples of Orders 8 and 16.
  2. Inder J. Taneja, Block-Wise Construction of Bimagic Squares Multiples of 25: Orders 25, 125 and 625.
  3. Inder J. Taneja, Block-Wise Construction of Bimagic Squares Multiples of 9: Orders 9, 81 and 729.
  4. Inder J. Taneja, Block-Wise Construction of Bimagic Squares of Orders 121 and 1331.
  5. Inder J. Taneja, Bimagic Squares of Orders 256, 512 and 1024: Blocks of Order 16.
  6. Inder J. Taneja, Bimagic Squares of Orders 200 and 1000: Blocks of Order 8
  7. Inder J. Taneja, Bimagic Squares of Orders 400, 800, 1600 and 2000: Blocks of Order 16.
  8. Aale de Winkel, Magic Encyclopedia magic square, magic cube, magic tesseract, magic hypercube.
  9. Christian Boyer, MULTIMAGIE.COM – Bimagic squares, 10th and 11th-Order. (Fredrik Jansson).

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