Vedic square

In ancient Indian mathematics, a Vedic square is a special type of 9 × 9 multiplication table. Like the ordinary multiplication table in the decimal system, it is a square grid where rows and columns are headed by the numbers to multiply, and the entry in each cell is the product of the column and row headings. However, in a Vedic square, the entry in each cell is the digital root of the product of the column and row headings i.e. the remainder when the product of the row and column headings is divided by 9 (with remainder 0 represented by 9). Like the normal 3 × 3 magic square, 9 × 9 Latin square, and 9 × 9 Sudoku, all the entries are the numbers 1 through 9. Numerous geometric patterns and symmetries can be observed in a Vedic square.

Example

×	1	2	3	4	5	6	7	8	9
1	1	2	3	4	5	6	7	8	9
2	2	4	6	8	1	3	5	7	9
3	3	6	9	3	6	9	3	6	9
4	4	8	3	7	2	6	1	5	9
5	5	1	6	2	7	3	8	4	9
6	6	3	9	6	3	9	6	3	9
7	7	5	3	1	8	6	4	2	9
8	8	7	6	5	4	3	2	1	9
9	9	9	9	9	9	9	9	9	9

See also

• Modular arithmetic