It is said that even you who has graduated from High School will say WOW! when you saw this:
Katanya nih... walaupun kamu sudah lulus SMU, kamu tetep bakal bilang WOW! waktu kamu lihat ini:
All the result are ONEs, boriiiiing...
Semua angka satu, bosaaaaan...
0 x 9 + 1 = 1
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
123456789 x 9 + 10 = 1111111111
The first one is usually boring. Actually, old people thought a way to test calculator's performance with:
Pertama memang biasanya membosankan. Sebenarnya, orang dulu pernah memikirkan cara menguji kinerja kalkulator dengan:
12345679 x 9 = 111111111
... but, this doesn't work anymore, I think.
... tapi, kurasa ini ga berguna lagi.
Look, it's mirroring...
Lihat, angka-angka ini seperti dicerminkan...
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 = 1234567898765432
Another Magic of Math...
Keajaiban Matematika yang lain...
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
Then... Check this out...
Lalu... Coba lihat yang ini...
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
Try this one....
Coba yg ini....
123456789 + 987654321 = 1111111110
1 x 142857 = 142857
2 x 142857 = 285714
3 x 142857 = 428571
4 x 142857 = 571428
5 x 142857 = 714285
6 x 142857 = 857142
7 x 142857 = 999999
Wow.... what a fantastic result
Waw.... hasil yang Fantastis
All have same numbers but different positions.
Semua angkanya sama tapi letak beda.
This is what we do when we were still in elementary school... have you ever known?
If we multiply any number with 9, then we add up each digit of the result until it only has 1 digit, the digit is always 9. Let's prove it...
Ini adalah cara SD... udah tau belum?
bilangan sembarang jika dikalikan 9 lalu hasilnya dijumlah lagi sampai tinggal satu angka, pasti angka itu 9. Kita buktikan...
1 x 9 = 9
2 x 9 = 18, (addition) (jumlah) 1 + 8 = 9
3 x 9 = 27, (addition) (jumlah) 2 + 7 = 9
11 x 9 = 99, (addition) (jumlah) 9 + 9 = 18 (addition) (jumlah) 1 + 8 = 9 (still "= 9") (tetep "= 9" kan?)
and so on until infinity... is this interesting?
dst. sampai tak terhingga... OK kan?
There are some foolish game by a foolish magician (actually he is not really foolish because some kids still get excited with it), example:
"Hey, I have an interesting game, it's about numbers and whose kid doesn't like numbers? Try to imagine a number between 2 to 10 in your brain! Listen to me carefully, keep the number in your brain, just for yourself, don't tell anybody! Then... multiply it with 9. Could you do it? because if you can't, you are gonna need to use my calculator. Then... Add the first number with the last number for example if your result is 14 (even only stupid kids will have this result), add 1 with 4, still keep the result in your brain! Divide it with 3... substract it with 1... have you done?"
The foolish magician said, "The result must be two, am I correct?"
then the kids get excited and respond, "How do you do that?"
Ada permainan bodoh yang dilakukan oleh pesulap bodoh (sebenarnya dia tidak sebodoh itu sich karena beberapa anak kecil tetap saja tertarik untuk menyimaknya), contoh:
"Hai anak-anak, aku punya permainan menarik, ini adalah permainan tentang angka, siapa yang ga suka angka? Coba bayangkan sebuah angka antara 2 sampai 10 dalam pikiran kamu, hanya dalam pikiran kamu, jangan beritahu siapa-siapa yah! Coba kalikan angka tersebut dengan 9. Bisakah kamu melakukannya? Kalau kamu ga bisa, aku pikir kamu perlu kalkulator. Lalu, tambahkan angka pertama dengan angka terakhir, contoh: kalau hasilnya 14 (walaupun hanya anak bodoh saja yang akan dapat hasil seperti ini), tambahkan 1 dengan 4, lalu simpan hasilnya di dalam otak kamu! Bagi tiga... kurangi satu... sudah selesai?"
Pesulap Bodoh berkata, "Hasilnya pasti sama dengan dua, benar?"
lalu anak-anak pun takjub dan berkata, "Bagaimana kamu melakukannya
more....
ada lagi....
22 x 9 = 198,
the easy way is 2 x 9 = 18, then put 9 between the numbers, the result is 198....ok?
prove these by yourself...
cara cepatnya 2 x 9 = 18, lalu selipkan angka 9 ditengah, jadi 198....ok?
buktikan sendiri cara cepatnya berikut ini...
33 x 9 = 297 (eg.: 3 x 9 = 27, put 9 in the middle) (contoh: 3 x 9 = 27, 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
this is similar, just put 99 in the middle....
you don't believe me...? let's prove it!
sama aja tuch tinggal selipkan 99 ditengahnya....
gak percaya...? kita buktikan yach...
222 x 9 = 1998 (eg.: 2 x 9 = 18, put 99 between) (contoh: 2 x 9 = 18, selipkan 99 ditengah)
333 x 9 = 2997
444 x 9 = 3996
555 x 9 = 4995
The last...
Terakhir...
9^1 = 9
9^2 = 81 = 8+1= 9
9^3 = 729 = 7+2+9 = 18 = 1+8 = 9
9^4 = 6561 = 6+5+6+1 = 18 = 1+8 = 9
9^5 =59049 = 5+9+0+4+9 =27 = 2+7 = 9
9^6 = 531441 = 5+3+1+4+4+1 = 18 = 1+8 = 9
9^7 = 4782969 = 4+7+8+2+9+6+9 = 45 = 4+5 = 9
9^8 = 43046721 = 4+3+0+4+6+7+2+1 = 27 = 2+7 = 9
9^9 = ....isi sendiri
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