There are many ways of representing magic squares with palindromic type entries. Also, we can write magic squares in the composite forms based on pair of Latin squares. This paper works with magic squares of order 3 to 6. By **upside-down**, we understand than by making 180^{o} it remains same. When the magic square is of both type, i.e., **upside-down** and **mirror looking**, we call it an **universal** magic square. By mirror looking we understand that putting in front of mirror, still we see the image as a magic square. In case of mirror looking, writing as **digitais fonts**, 2 becomes 5 and 5 as 2. In case of **upside-down**, 6 becomes 9 and 9 as 6.

The magic squares of 9, we have considered in two different situations. One as **bimagic** and another as **pandiagonal**. In case of order 8, we considered the situations with **pandiagonal** and **bimagic**. The orders 7 to 10 are considered in another work. See the links below:

**Inder J. Taneja**, Universal and Upside-Down Magic Squares of Orders 3 to 6,**Zenodo**, September 30, 2024, pp. 1-59, https://doi.org/10.5281/zenodo.13858891.**Inder J. Taneja**, Universal and Upside-Down Magic Squares of Orders 7 to 10,**Zenodo**, September 30, 2024, pp. 1-87, https://doi.org/10.5281/zenodo.13858893.

### Magic Squares of Order 3

### a) 2-Digits Cell Entries:

**Example 1.**

It is **upside-down** **semi-magic** square of order 3 with 3-digits (1,6,9). The magic sum is **S _{3×3}(1,6,9):=176.** This magic square becomes becomes

**semi-magic**in case of

**mirror looking**.

**Example 2.**

It is **universal** magic square of order 3 with 3-digits (2,5,8). The magic sum is **S _{3×3}(2,5,8):=165.** This magic square becomes becomes

**semi-magic**in case of

**mirror looking**.

### b) 3-Digits Cell Entries:

**Example 3.**

It is **upside-down** **semi-magic** square of order 3 with 3-digits (1,6,9). In this case, the entries are **palindromes.** The magic sum is **S _{3×3}(1,6,9):=1776.**

**Example 4.**

It is **universal** magic square of order 3 with 3-digits (2,5,8). The magic sum is **S _{3×3}(2,5,8):=1665.** In this case, the entries are

**palindromes.**This magic square becomes becomes

**semi-magic**in case of

**mirror looking**.

### Magic Squares of Order 4

### a) 2-Digits Cell Entries:

**Example 5.**

It is **upside-down** magic square of order 4 with 4-digits (1,6,8,9). The magic sum is **S _{4×4}(1,6,8,9):=264.**

**Example 6.**

It is **universal ** magic square of order 4 with 4-digits (0,1,2,5). The magic sum is **S _{4×4}(0,1,2,5):=88.**

It is well-known author’s stamp published at Macau – China – 2015. See below:

### b) 3-Digits Cell Entries:

**Example 7.**

It is **upside-down** magic square of order 4 with 4-digits (1,6,8,9). In this case, the entries are **palindromes**. The magic sum is **S _{4×4}(1,6,8,9):=2664.**

**Example 8.**

It is **universal **magic square of order 4 with 4-digits (1,2,5,8). In this case, the entries are **palindromes**. The magic sum is **S _{4×4}(1,2,5,8):=1776.**

### c) 4-Digits Cell Entries:

**Example 9.**

It is **pandiagonal** **upside-down** magic square of order 4 with 2-digits (6,9). The magic sum is **S _{4×4}(6,9):=33330.**

**Example 10.**

It is **pandiagonal universal **magic square of order 4 with 2-digits (1,8). The magic sum is **S _{4×4}(1,8):=19998.**

**Example 11.**

It is **pandiagonal** **universal **magic square of order 4 with 2-digits (2,5). The magic sum is **S _{4×4}(2,5):=15554.**

### d) 7-Digits Cell Entries:

**Example 12.**

It is **pandiagonal** **upside-down** magic square of order 4 with 2-digits (6,9). The entries are **palindromes**. The magic sum is **S _{4×4}(6,9):=33333330.**

**Example 13.**

It is **pandiagonal universal **magic square of order 4 with 2-digits (1,8). The entries are **palindromes**. The magic sum is **S _{4×4}(1,8):=19999998.**

**Example 14.**

It is **pandiagonal universal **magic square of order 4 with 2-digits (2,5). The entries are **palindromes**. The magic sum is **S _{4×4}(2,5):=15555554.**

### Magic Squares of Order 5

### a) 5-Digits Cell Entries:

**Example 15.**

It is **pandiagonal** **upside-down** magic square of order 5 with 5-digits (0,1,6,8,9). The magic sum is **S _{5×5}(0,1,6,8,9):=264.**

**Example 16.**

It is **pandiagonal** **upside-down** magic square of order 5 with 5-digits (2,5,6,8,9). The magic sum is **S _{5×5}(2,5,6,8,9):=330.**

**Example 17.**

It is **pandiagonal** **universal** magic square of order 5 with 5-digits (0,1,2,5,8). The magic sum is **S _{5×5}(0,1,2,5,8):=176.**

### b) 3-Digits Cell Entries:

**Example 18.**

It is **pandiagonal** **upside-down** magic square of order 5 with 5-digits (1,2,5,6,9). In this case the entries are **palindromes**. The magic sum is **S _{5×5}(1,2,5,6,9):=2553.**

**Example 19.**

It is **pandiagonal** **universal **magic square of order 5 with 5-digits (0,1,2,5,8). In this case the entries are **palindromes**. The magic sum is **S _{5×5}(0,1,2,5,8):=1776.**

### c) 4-Digits Cell Entries:

**Example 20.**

It is **pandiagonal** **upside-down** magic square of order 5 with 3-digits (1,6,9). The magic sum is **S _{5×5}(1,6,9):=34441.**

**Example 21.**

It is **pandiagonal** **upside-down** magic square of order 5 with 3-digits (6,8,9). The magic sum is **S _{5×5}(6,8,9):=42218.**

**Example 22.**

It is **pandiagonal** **universal ** magic square of order 5 with 3-digits (2,5,8). The magic sum is **S _{5×5}(2,5,8):=24442.**

### Magic Squares of Order 6

### a) 4-Digits Cell Entries:

**Example 23.**

It is **upside-down** magic square of order 5 with 3-digits (6,8,9). The magic sum is **S _{6×6}(2,5,8):=33330.** This magic square is only

**upside-down**because its

**mirror looking image**is no more a

**magic square.**