** Whole the work is done manually on excel sheets**.

Below are **bimagic squares** written in blocks multiples of orders 8. These are bimagic squares of order 200 and 1000. Most of the work is done manually by author in 2011. **Inder J. Taneja**, Bimagic Squares of Bimagic Squares and an Open Problem, Febuarary 11, 2011, 2011, pp. 1-14, (22.02.2011), https://doi.org/10.48550/arXiv.1102.3052.

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.

### Bimagic Square of Order 8

In this case, we have

**S _{8×8}:=260; Sb_{8×8}:= 11180**

2×4 blocks are of equal sums as of magic square, i.e., 260. See below the **bimagic square** of order 8.

*The construction of *bimagic* square of order 8 is well known in the history, and is done by G. Pfeffermann in 1891. In this case, we have a pandiagonal bimagic square of order 8, where the blocks of order 2×4 are of same sum as of magic square of order 8.*

### Bimagic Square of Order 40: Blocks of Order 8

In this case, we have

**S _{40×40}:=32020; Sb_{40×40}:= 34165340, S_{8×8}:=6404.**

Magic squares of order 8 are of equal sums. These are either bimagic or semi-bimagic. See **bimagic square** of order 40. It is also pandiagonal.

### Bimagic Square of Order 200: Blocks of Orders 8 and 40

**Bimagic square of order 200×200** has the the following properties:

- 8×8 are
**pandiagonal magic squares**with**equal magic sums**, i.e.,**S**. These are with different bimagic or semi-bimagic sums._{8×8}:=160004 - 40×40 are
**pandiagonal equal sums magic squares**with different**bimagic sums,**i.e.,**S**. These are with different bimagic or semi-bimagic sums._{40×40}:=800020 - 200×200 is a
**pandiagonal bimagic squares**with**magic and bimagic sums S**and_{200×200}:=4000100**Sb**._{200×200}:=106670666700

Summarizing, we have a **pandiagonal bimagic square of order 200×200**, where blocks of orders 8×8 and 40×40 are also pandiagonal with equal magic sums, but different bimagic or semi-bimagic sums. These values are given in tables in an excel sheet attached with the work.

**Excel file for download**

### Bimagic Square of Order 1000: Blocks of Orders 8, 40 and 200

**Bimagic square of order 1000×1000** has the the following properties:

- 8×8 are
**pandiagonal equal sums magic squares**, i.e.,**S**. These are with different bimagic or semi-bimagic sums._{8×8}:=4000004 - 40×40 are
**pandiagonal equal sums magic squares**, i.e.,**S**. These are with different bimagic or semi-bimagic sums._{40×40}:=20000020 - 200×200 are pandiagonal
**equal sum magic squares**, i.e,These are with different bimagic or semi-bimagic sums.**S**100000100._{200×200}:= - 1000×1000 is a
**pandiagonal bimagic square**with magic and bimagic sums,**S**and_{1000×1000}:=500000500.**Sb**:=333333833333500_{1000×1000}

Summarizing, we have a **pandiagonal bimagic square of order 1000×1000**, where blocks of orders 8×8, 40×40 and 200×200 are also pandiagonal with equal magic sums, but different bimagic or semi-bimagic sums. These values are given in tables in an excel sheet attached with the work.

**Excel file for download**

### References:

**Inder J. Taneja,**Block-Wise Construction of Bimagic Squares: Multiples of Orders 8 and 16.**Inder J. Taneja,**Block-Wise Construction of Bimagic Squares Multiples of 25: Orders 25, 125 and 625.**Inder J. Taneja,**Block-Wise Construction of Bimagic Squares Multiples of 9: Orders 9, 81 and 729.**Inder J. Taneja,**Block-Wise Construction of Bimagic Squares of Orders 121 and 1331.**Inder J. Taneja,**Bimagic Squares of Orders 256, 512 and 1024: Blocks of Order 16.