12.345.679
x 9 =111.111.111
12.345.679 x
18 =222.222.222
12.345.679 x 27
=333.333.333
12.345.679 x 36
=444.444.444
12.345.679 x 72
= 888.888.888
12.345.679 x 81 =
999.999.999
12=
1
112= 121
1112= 12321
11112= 1234321
111112= 123454321
1111112= 12345654321
11111112= 1234567654321

1=12
1+3=
22
1+3+5=
32
1+3+5+7=
42
1+3+5+7+9=
52
1+3+5+7+9+11=
62

1+2=
3
4+5+6=
7+8
9+10+11+12=
13+14+15
16+17+18+19+20=
21+22+23+24

4913=(4+9+1+3)3
5832=(5+8+3+2)3
19683=(1+9+6+8+3)3
17576=(1+7+5+7+6)3
390265=(3+9+0+6+2+5)4
234256=(2+3+4+2+5+6)4

25.92 = 2592
13+53+33=153
33+73+13=371

32
+ 42 = 52
102 + 112 + 122 = 132 + 142
212 + 222 + 232 + 242 = 252
+ 262 + 272
362 + 372 + 382 + 392 + 402
= 412 + 422 + 432 + 442

Üç basamaklı herhangi
bir sayıyı iki kere yan yana yazarak elde ettiğimiz yeni sayı,
kesinlikle
7, 11, 13, 77, 91, 143, 1001
sayılarına kalansız olarak bölünür(neden?).
Örnek: 831831
831831 / 7 = 118833
831831 / 11 = 75621
831831 / 13 = 63987
831831 / 77 = 10803
831831 / 91 = 9141
831831 / 143 = 5817
831831 / 1001 = 831

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
12
x 42 =
21
x 24
23
x 96 =
32
x 69
24
x 84 =
42
x 48
13
x 62 =
31
x 26
46
x 96 =
64
x 69

(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
(987654321 x 9) - 1 = 8888888888

1 . 1 =
1
11 . 11 = 121
111 . 111 = 12321
1111 . 1111 = 1234321
11111 . 11111 = 123454321

123456789 . 9 = 11 111 111
123456789 . 18 = 222 222 222
123456789 . 27 = 333 333 333

4913 =
(4+9+1+3)3
5832 = (5+8+3+2)3
19683 = (1+9+6+8+3)3
17576 = (1+7+5+7+6)3
390265 = (3+9+0+6+2+5)4
234256 = (2+3+4+2+5+6)4

52521875 = (5+2+5+2+1+8+7+5)5
135 = 1.3.5.(1+3+5)
144 = 1.4.4.(1+4+4)
8833 = 882 + 332
7744 = 88.88

987654321 *
09
= 08.888.888.889
987654321 * 18
= 17.777.777.778
987654321 * 27
= 26.666.666.667
987654321 * 36
= 35.555.555.556
987654321 * 45
= 46.666.666.665
987654321 * 54
= 57.777.777.774
987654321 * 68
= 68.888.888.883
987654321 * 72
= 79.999.999.992
987654321 * 81
= 80.000.000.001
