Keunikan Bilangan 6 dan 9

Dengan menggunakan operasi aritmatik biasa (seperti +, -, *, dan /) ternyata kita akan menemukan bilangan-bilangan yang memiliki keunikan. Berikut ini beberapa keunikan bilangan 6 dan 9 yang saya kutip dari faqih.net

Keunikan bilangan 6 :

1 + 2 + 3 + 4 + 5 + 6 = 21

1 + 2 + 3 + …….+ 66 = 2211

1 + 2 + 3 + …….+ 666 = 222111

1 + 2 + 3 + …….+ 6666 = 22221111

1 + 2 + 3 + …….+ 66666 = 2222211111

1 + 2 + 3 + …….+ 666666 = 222222111111



Berdasarkan contoh tersebut, cobalah untuk menyelesaikan soal berikut

1 + 2 + 3 + …+ n = 222…222111…111 (masing-masing angka 1 dan 2 muncul 2011 kali)

Tentukan nilai n

Beberapa fakta matematika tentang bilangan 666:

* Merupakan bilangan palindrome
* Jumlah 36 bilangan asli yang pertama, 1+2+3+4..….+35+36 =666
* Banyak bilangan prima yang kurang dari 666 adalah 121. 121 = 112.
* 6=(32) − (22) + 1
* 66=(34) − (24) + 1
* 666=(36) − (26) + 1
* The total of the amount of the first seven prime numbers square, ie : 22 + 32 + 52 + 72 + 112 + 132 + 172 = 666
* In Roman numerals, 666 represented as DCLXVI (D = 500, C = 100, L = 50, X = 10, V = 5, I = 1). DIC LVX is a representation of dicit lux. Dicit lux later known as the voice of light.

Bilangan 9

1. Perkalian dengan 9, 99, 999, …

Contoh 1

63 x 99 = 63 ( 100 – 1 )

= 63. 100 – 63. 1

= 6300 – 63

= 6237

Contoh 2

999 x 27 = (1000 – 1) x 27

= 2700 – 27

= 26.973

Beberapa Keunikan 9

1, Keunikan 1

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

Keunikan 2

Daftar hasil kali bilangan 987654321 dengan sembilan bilangan asli kelipatan 9 yang pertama tampak seperti berikut :

987654321 x 9 = 8.888.888.889

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


Keunikan 3

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


Keunikan 4

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


Keunikan 5

0 x 9 + 0 = 0

1 x 9 + 1 = 10

12 x 9 + 2 = 110

123 x 9 + 3 = 1110

1234 x 9 + 4 = 11110

12345 x 9 + 5 = 111110

123456 x 9 + 6 = 1111110

1234567 x 9 + 7 = 11111110

12345678 x 9 + 8 = 111111110

123456789 x 9 + 9 = 1111111110


Keunikan 6

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


Keunikan 8

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


Keunikan 9

1 x 18 + 1 = 19

12 x 18 + 2 = 218

123 x 18 + 3 = 2217

1234 x 18 + 4 = 22216

12345 x 18 + 5 = 222215

123456 x 18 + 6 = 2222214

1234567 x 18 + 7 = 22222213

12345678 x 18 + 8 = 222222212

123456789 x 18 + 9 = 2222222211

123456789 + 987654321 = 1111111110

Keunikan 10

1 x 142857 = 142857 (bilangan sama)

2 x 142857 = 285714 (bilangan sama, urutan berbeda )

3 x 142857 = 428571 (bilangan sama, urutan berbeda )

4 x 142857 = 571428 (bilangan sama, urutan berbeda )

5 x 142857 = 714285 (bilangan sama, urutan berbeda )

6 x 142857 = 857142 (bilangan sama, urutan berbeda )

7 x 142857 = 999999 (fantastic result!)


Keunikan 11

1 x 9 = 9

2 x 9 = 18, result of 1 + 8 = 9

3 x 9 = 27, result of 2 + 7 = 9

4 x 9 = 36, result of 3 + 6 = 9

5 x 9 = 45, result of 4 + 5 = 9

6 x 9 = 54, result of 5 + 4 = 9

7 x 9 = 63, result of 6 + 3 = 9

8 x 9 = 72, result of 7 + 2 = 9

9 x 9 = 81, result of 8 + 1 = 9

10 x 9 = 90, result of 9 + 0 = 9, and so on., till infinity.

Keunikan 12

22 x 9 = 198,

the fast way is 2 x 9 = 18, then insert number 9 in the middle, become 198.

33 x 9 = 297

44 x 9 = 396

55 x 9 = 495

66 x 9 = 594

77 x 9 = 693

88 x 9 = 792

99 x 9 = 891


Keunikan 13

222 x 9 = 1998, fast way: 2 x 9 = 18, insert 99 in the middle.

333 x 9 = 2997

444 x 9 = 3996

555 x 9 = 4995


http://labarasi.wordpress.com/2011/11/06/keunikan-bilangan-6-dan-9/