## Saturday, November 27, 2010

### Magic of numbers

Could you explain the following results:

7 * 7 = 49
67 * 67 = 4489
667 * 667 = 444889
6667 * 6667 = 44448889
66667 * 66667 = 4444488889
666667 * 666667 = 444444888889
6666667 * 6666667 = 44444448888889

4 * 4 = 16
34 * 34 = 1156
334 * 334 = 111556
3334 * 3334 = 11115556
33334 * 33334 = 1111155556
333334 * 333334 = 111111555556

9 * 9 = 81
99 * 99 = 9801
999 * 999 = 998001
9999 * 9999 = 99980001
99999 * 99999 = 9999800001
999999 * 999999 = 999998000001
9999999 * 9999999 = 99999980000001

7 * 9 = 63
77 * 99 = 7623
777 * 999 = 776223
7777 * 9999 = 77762223
77777 * 99999 = 7777622223
777777 * 999999 = 777776222223

1 * 7 + 3 = 10
14 * 7 + 2 = 100
142 * 7 + 6 = 1000
1428 * 7 + 4 = 10000
14285 * 7 + 5 = 100000
142857 * 7 + 1 = 1000000
1428571 * 7 + 3 = 10000000
14285714 * 7 + 2 = 100000000
142857142 * 7 + 6 = 1000000000
1428571428 * 7 + 4 = 10000000000
14285714285 * 7 + 5 = 100000000000
142857142857 * 7 + 1 = 1000000000000

7 * 15873 = 111111
14 * 15873 = 222222
21 * 15873 = 333333
28 * 15873 = 444444
35 * 15873 = 555555
42 * 15873 = 666666
49 * 15873 = 777777
56 * 15873 = 888888
63 * 15873 = 999999

91 * 1221 = 111111

900991 * 123321 = 111111111111

#### 1 comment:

1. the one starting with "1*7 + 3 = 10":

i don't have an answer for you, but i will point out that ".142857142857..." is exactly 1/7. since your whole scheme here revolves around (a) 1/7 as a decimal, but with no decimal point and (b) multiplying by 7 and (c) adding numbers less than 7 [remainders, no doubt], this looks like it is definitely important. more thought will be necessary.