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Nine times nine

In China the multiplication tables are called the "nine times nine is eighty one" and are learned like a song with 45 lines of 5 words each.

 


Explanation

There are 81 lines, but if you omit the duplicates, there remain only 45.

1 × 1 =  1
1 × 2 =  2
2 × 2 =  4
1 × 3 =  3
2 × 3 =  6
3 × 3 =  9
1 × 4 =  4
2 × 4 =  8
3 × 4 = 12
4 × 4 = 16
1 × 5 =  5
2 × 5 = 10
3 × 5 = 15
4 × 5 = 20
5 × 5 = 25
1 × 6 =  6
2 × 6 = 12
3 × 6 = 18
4 × 6 = 24
5 × 6 = 30
6 × 6 = 36
1 × 7 =  7
2 × 7 = 14
3 × 7 = 21
4 × 7 = 28
5 × 7 = 35
6 × 7 = 42
7 × 7 = 49
1 × 8 =  8
2 × 8 = 16
3 × 8 = 24
4 × 8 = 32
5 × 8 = 40
6 × 8 = 48
7 × 8 = 56
8 × 8 = 64
1 × 9 =  9
2 × 9 = 18
3 × 9 = 27
4 × 9 = 36
5 × 9 = 45
6 × 9 = 54
7 × 9 = 63
8 × 9 = 72
9 × 9 = 81

In the table of Pythagoras you find them all.

1 2 3 4 5 6 7 8 9
2 4 6 8 10 12 14 16 18
3 6 9 12 15 18 21 24 27
4 8 12 16 20 24 28 32 36
5 10 15 20 25 30 35 40 45
6 12 18 24 30 36 42 48 54
7 14 21 28 35 42 49 56 63
8 16 24 32 40 48 56 64 72
9 18 27 36 45 54 63 72 81

 


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