Ramanujan Magic Square for 15/09/2025

Published:

Row Sums:

  1. 15 + 9 + 20 + 25 = 69

  2. 26 + 19 + 6 + 18 = 69

  3. 7 + 17 + 27 + 18 = 69

  4. 21 + 24 + 16 + 8 = 69
    All rows sum to 69


Column Sums:

  1. 15 + 26 + 7 + 21 = 69

  2. 9 + 19 + 17 + 24 = 69

  3. 20 + 6 + 27 + 16 = 69

  4. 25 + 18 + 18 + 8 = 69
    All columns sum to 69


Diagonal Sums:

  • Main Diagonal: 15 + 19 + 27 + 8 = 69

  • Anti-Diagonal: 25 + 6 + 17 + 21 = 69
    Both diagonals sum to 69

Entry #607

Comments

Avatar tokecap -
#1
A. Extract Rows, Columns, Diagonals

Use rows, columns, and diagonals as ready-made number groups:

? Pick 3:

From your square:

[15, 9, 20, 25]
[26, 19, 6, 18]
[7, 17, 27, 18]
[21, 24, 16, 8]


You can extract:

Rows: 159, 926, 718, 241

Columns: 157, 919, 206, 258

Diagonals: 15 19 27, 25 6 17

Resulting Pick 3 Ideas (using last digits or trimmed):

159 ? 1-5-9

926 ? 9-2-6

718 ? 7-1-8

241 ? 2-4-1

197 ? 1-9-7

256 ? 2-5-6

You can:

Use last digits only (e.g. 25 ? 5, 27 ? 7)

Use digit sums (e.g. 15 ? 1+5 = 6)

? Pick 4:

Same logic, but use full rows/columns:

Row 1: 15-9-20-25 ? 1-5-9-2

Row 2: 26-19-6-18 ? 2-6-1-8

Diagonal: 15-19-27-8 ? 1-9-2-8

B. Digit Splitting

Split every 2-digit number into single digits:

Magic Square flattened:
15, 9, 20, 25, 26, 19, 6, 18, 7, 17, 27, 18, 21, 24, 16, 8
? Digits: 1,5,9,2,0,2,5,2,6,1,9,6,1,8,7,1,7,2,7,1,8,2,1,2,4,1,6,8


Now generate combinations:

Random 3-digit sets: e.g. 1-9-6, 2-5-8, etc.

Pick 4: group every 4 sequential digits: 1-5-9-2, 0-2-5-2, etc.

C. Sums and Roots

Use numerology-style reductions:

Number Sum Root
15 6 6
9 9 9
20 2 2
25 7 7
...

Use combinations of sums or roots as your pick 3:

Root combos: 6-9-2, 7-1-6, etc.

D. Directional Movement

Start from any cell and move:

Horizontally (L?R or R?L)

Vertically (U?D)

Diagonally

Knight moves (chess-style)

Example:

Starting at 15 ? go right ? 9 ? 20 ? 25 ? 159, 920, 025

Apply filter rules:

Use only combinations with no repeats

Use only odd/even balances

High/low splits

E. Difference Patterns

Calculate difference between adjacent cells in rows/cols:

Row 1: 15, 9, 20, 25 ? Differences: 6, 11, 5 ? Combo: 6-1-5

Col 1: 15, 26, 7, 21 ? Diff: 11, 19, 14 ? Combo: 1-9-4

Great way to get hidden patterns.

F. Frequency Chart (Digit-Level)

Count how often each digit (0–9) appears across the square.
Helps build weighted wheels or biased picks.

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