Maths is Fun ( MERGED with Cherry's)

Erm, not really..
if you use the correct method,
won't take you more than 10 minutes to find the smallest such integer,
and if you spend another 10-15 minutes, you can notice a pattern.

Oh yeah,
btw, I did that question last year, while waiting for my STPM results.
Maybe you were right also in saying that i am too free.
Haha.

First of all, notice that the last digit must be from 2 - 9.
It cannot be 1 because if we move it to the front, it cannot be twice the original number. (Number of digits stay the same)

so, lets us start with the last digit being 2,
which means the first digit must be 1.

By doing multiplication

1................................................................... 2
x                                                                    2
                                                                     4

we get 4 as the last digit after multiplication by 2, which means the 2nd last digit must be 4.
Continuing the process,

105263157894736842
x                            2
210526315789473684

Now, we have one such number 105263157894736842

one thing interesting is that after you get 210526315789473684
and you move the last digit to the front again,
you get 421052631578947368 which is twice 210526315789473684
and when you move 8 to the front,
you get 842105263157894736 which is twice 421052631578947368

and when you use 3 as the last digit and 1 as the first digit,
it is easy to see that 157894736842105263 is another such number,
and so on.
By viewing the number as a cycle and arbitraryly pick a digit from 1 - 4 as the starting digit, we can generate a new number with similar characteristic from the number itself.


P/S: I hope what I just said is not confusing. The concept is just doing simple multiplication. Oh, and this is just for fun, I don't think there is any useful application for this kind of numbers, or this kind of solving method.

...how complicated maths can be...but if u know the rules...it's really fun actually...
...zillion thanks to amorist...forgiv...mbhcsf(must be stand for something this acronym)...dockers guy...sarah radzi...and the rest...

By Charles R. Darwin (1809-1882) [English biologist]

"A mathematician is a blind man in a dark room looking for a black cat
which isn't there"

Personally, I dont think it is that bad. lol
Oh, and really, no offence to the mathematicians.

...a biologist??...Darwin Theory...said that!!...what an irony!!...:bgrin:...

mareenie

This is the beauty of MATHS

cuba selesaikan masalah berikut :-

Q1 : one divide by one?
Q2 : one divide by zero?
Q3 : zero divide by one?
Q4 : zero divide by zero?

kenapa, mengapa dan bagaimana?

Originally posted by spinzero at 18-7-2004 15:19:
cuba selesaikan masalah berikut :-

Q1 : one divide by one?
Q2 : one divide by zero?
Q3 : zero divide by one?
Q4 : zero divide by zero?

kenapa, mengapa dan bagaimana?

Ape masalahnye nih? Macam takde problem langsung pun

padlie

Untuk dikongsi bersama bagi yang belum tahu...

A)

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




B)

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




C)

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




D)

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




E)

123456789 + 987654321 = 1111111110




F)

1 x 142857 = 142857

2 x 142857 = 285714 (angka sama susunan berbeza)

3 x 142857 = 428571 (angka sama susunan berbeza)

4 x 142857 = 571428 (angka sama susunan berbeza)

5 x 142857 = 714285 (angka sama susunan berbeza)

6 x 142857 = 857142 (angka sama susunan berbeza)

7 x 142857 = 999999 (wauuu......Fantastikkk)




G)

Sebarang nilai jika dikalikan 9 maka jumlah hasilnya = 9 kita buktikan.....

1 x 9 = 9

2 x 9 = 18, jumlah 1 + 8 = 9

3 x 9 = 27, jumlah 2 + 7 = 9

4 x 9 = 36, jumlah 3 + 6 = 9

dst. sampai tak terhingga.....



H)

22 x 9 = 198.....cara cepatnya 2 x 9 = 18, lalu selitkan angka 9 ditengah, jadi 198....

buktikan sendiri cara cepat ini...

33 x 9 = 297, cara cepat 3 x 9, selipkan 9 ditengah

44 x 9 = 396

55 x 9 = 495

66 x 9 = 594

77 x 9 = 693

88 x 9 = 792

99 x 9 = 891




I)

Jika 3 angka kembar pula, selitkan angka 99 ditengahnya ....

kita buktikan......

222 x 9 = 1998, cara cepat 2 x 9= 18, selitkan 99 ditengah

333 x 9 = 2997

444 x 9 = 3996

555 x 9 = 4995

Satria-Naga

Originally posted by padlie at 23-4-2005 11:26 AM:
Untuk dikongsi bersama bagi yang belum tahu...

A)

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 ...

Interesting! :bgrin:

Robab

wow!!!
best tol

mobalinbong

Originally posted by padlie at 23-4-2005 12:26 PM:
Untuk dikongsi bersama bagi yang belum tahu...

A)

0 x 9 + 0 = 0

best2 ...bravo........

Sarah_Radzi

seri nombor tu ada yang ada nama : cf bawah (takes part partly or totally)

B) Wonderful Demlo numbers, Odd number of digits palindrome based on sequential digits,   Smallest square beginning with concatenation of first n natural numbers.

C) http://www.research.att.com/projects/OEIS?Anum=A064617

F) http://www.research.att.com/projects/OEIS?Anum=A101202

[ Last edited by Sarah_Radzi on 23-4-2005 at 11:19 AM ]

bb_nessa

emm... series of number.. :hmm:

Atomic_Omnikid

two thumbs up..

tashieeya

hi
try to go to this website
http://mathsite.math.berkeley.ed ... tranceOverture.html
interesting

Eastern

Just for fun....

3,6,9,12,..... <-- Semua bleh teka apa nombor seterusnya,kan??

Sekarang,

O,T,T,F,F,S,S,E,N,.... <-- Saper bleh teka huruf seterusnya??

adlismel

Goldbach's conjecture says that every positive even number greater than 2 is the sum of two prime numbers. Example: 28 = 5 + 23. It is one of the most famous facts in number theory that has not been proved to be correct in the general case

menarik juga goldbach ni punya teori


contoh lain :

44 = 31 + 3

[ Last edited by adlismel at 8-12-2005 10:19 AM ]

mbhcsf

Adli - aah thread ttg topik ni bukan dah ader ker by marquez? well anyway  kalau you boleh merge kan it would be  kindly appreacited - Thanks.

adlismel

adli dah cari dah.. sebelum post.. tapi tak der.... sebab tu adli bukak semula