Magic Numbers

Enjoy the magic of numbers and appreciate some incredible mathematical coincidences:

3 x 37 = 111
6 x 37 = 222
9 x 37 = 333
12 x 37 = 444
15 x 37 = 555
18 x 37 = 666
21 x 37 = 777
24 x 37 = 888
27 x 37 = 999

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


12345679 x 9 = 111 111 111
12345679 x 18 = 222 222 222
12345679 x 27 = 333 333 333
12345679 x 36 = 444 444 444
12345679 x 45 = 555 555 555
12345679 x 54 = 666 666 666
12345679 x 63 = 777 777 777
12345679 x 72 = 888 888 888
12345679 x 81 = 999 999 999


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



There is also the magic number 142857, which simply changes the order of its digits when multiplied -

142857 x 1 = 142857
142857 x 2 = 285714
142857 x 3 = 428571
142857 x 4 = 571428
142857 x 5 = 714285
142857 x 6 = 857142
Other interesting equations with number 142857 are:
142857 õ 7 = 999999
142 + 857 = 999
14 + 28 + 57 = 99
142857 squared is 20408122449. If we split this number in two (20408 122449) and add them up: 20408+122449 = 142857