keajaiban pengkuadratan bilangan perulangan 1
1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 1111111 = 1234567654321
11111111 x 11111111 = 123456787654321
111111111 x 111111111 = 12345678987654321
keajaiban perkalian dengan 9 yang menghasilkan perulangan 1
0 x 9 + 1 = 1
1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1111
1234 x 9 + 5 = 11111
12345 x 9 + 6 = 111111
123456 x 9 + 7 = 1111111
1234567 x 9 + 8 = 11111111
12345678 x 9 + 9 = 111111111
123456789 x 9 + 10 = 1111111111
keajaiban perkalian dengan 8 yang menghasilkan urutan mundur
1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321
keajaiban perkalian dengan 9 yang menghasilkan perulangan 8
0 x 9 + 8 = 8
9 x 9 + 7 = 88
98 x 9 + 6 = 888
987 x 9 + 5 = 8888
9876 x 9 + 4 = 88888
98765 x 9 + 3 = 888888
987654 x 9 + 2 = 8888888
9876543 x 9 + 1 = 88888888
98765432 x 9 + 0 = 888888888
keajaiban deret bilangan asli dua ruas
1 + 2 = 3
4 + 5 + 6 = 7 + 8
9 + 10 + 11 + 12 = 13 + 14 + 15
16 + 17 + 18 + 19 + 20 = 21 + 22 + 23 + 24
25 + 26 + 27 + 28 + 29 + 30 = 31 + 32 + 33 + 34 + 35
36 + 37 + 38 + 39 + 40 + 41 + 42 = 43 + 44 + 45 + 46 + 47 + 48
49 + 50 + 51 + 52 + 53 + 54 + 55 + 56 = 57 + 58 + 59 + 60 + 61 + 62 + 63
64 + 65 + 66 + 67 + 68 + 69 + 70 + 71 + 72 = 73 + 74 + 75 + 76 + 77 + 78 + 79 + 80
81 + 82 + 83 + 84 + 85 + 86 + 87 + 88 + 89 + 90 = 91 + 92 + 93 + 94 + 95 + 96 + 97 + 98 + 99
....
deret ini bisa diperluas hingga tak hingga
keajaiban perkalian 37 dengan kelipatan 3
37 x 3 = 111
37 x 6 = 222
37 x 9 = 333
37 x 12 = 444
37 x 15 = 555
37 x 18 = 666
37 x 21 = 777
37 x 24 = 888
37 x 27 = 999
keajaiban perkalian urutan bilangan tanpa delapan
12345679 x 9 = 111111111
12345679 x 18 = 222222222
12345679 x 27 = 333333333
12345679 x 36 = 444444444
12345679 x 45 = 555555555
12345679 x 54 = 666666666
12345679 x 63 = 777777777
12345679 x 72 = 888888888
12345679 x 81 = 999999999
keajaiban perkalian urutan bilangan mundur dengan kelipatan 9
987654321 x 9 = 08 888 888 889
987654321 x 18 = 17 777 777 778
987654321 x 27 = 26 666 666 667
987654321 x 36 = 35 555 555 556
987654321 x 45 = 44 444 444 445
987654321 x 54 = 53 333 333 334
987654321 x 63 = 62 222 222 223
987654321 x 72 = 71 111 111 112
987654321 x 81 = 80 000 000 001
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