Ahad, 16 Mei 2010

..lucky no. 9..

..and when I was in standard 2 in Jitra Primary School (established in 1905), my Maths Teacher, Cikgu Anuar told me about the patterns of dividable number.

He said that if a number ended up in the result of multiplication of 2, then the number will always be divisible by 2. For example 23438, 5468, 566, 28956238745876 are all divisible by 2.

And others are like the rule of 0 and 5 ending that can be divided by 5 such as 345, 560, 235 and also the rule of divisible by 10.

He then said briefly about the rule of numbers divisible by 4, in which if the last 2 digits of a number can be divided by 4, then the whole number can be divided by 4.

He also mentioned that if the last three digits of a number is dividable by 8, then the whole number can be divided by 8. For example 45512 can be divided by 8 because 512 can be divided by 8, and 78921072 can be divided by 8 because 072 can be divided by 8.

But the rule that intrigues my brain to work the most each time I saw a number is the rule of 9.

In the rule of 9, if the sum of digits in a number is 9, then the whole number is divisible by 9.

For example in the number 5674832, 5+6+7+4+8+3+2 = 26, and further addition of 2+6 is equal to 8, which is not 9. Hence the number 5674832 is not divisible by 9.

Other example is 45387, 4+5+3+8+7 = 18, and further addition 1+8= is 9. Therefore the number 45387 can be divided by 9.

The rule is simple, only addition. But the wonders of this result of addition that later determines is multiplicative value generates enough fuel for my brain to work whenever I saw numbers for the next 10 years.

And each time since that, whenever I saw a number my brain will automatically add it up to see whether it is divisible by 9. Any number that popped up infront of me was automatically added up for this reason. And the madness became overwhelmed when I am in the car on the street. On the road inside the car, especially in the highway, it's the heaven for numbers. What numbers? Car plate numbers!

My siblings always quarrel about who got to sit in the middle inside the car. But I, I chose to sit next to the window. When my father drove the car, I will put my chin on the window bar, and my eyes will hunt for the numbers at the back and front of each car. And the madness begun without stopping until we arrive at our destination. The madness of adding up car plate numbers.

And soon, the madness crazes when I am on the highway. Each time a car overtake our car, my eyes will quickly snap the car plate number, which passed impulse to my brain and quickly added up the digits. And the same goes whenever our car overtook other car. And the best part was when many cars overtake our car. It will squeeze the speed of my brain to work at its very best to quickly calculate the result each time 140 km/h cars passed one by one.

I also found out that any number that is added up to 9 will always result in the same number. For example 4+9=13, in which 1+3=4. And 6+9=15, in which 1+5=6.

Oh and the adrenaline, or it is other neurotransmitters?

After about 2 years of that unstoppable habit, my brain started to recognize new patterns. For example in the decimal numbers below,


the opposite pairs from each end of the digits are divisible by 9, that is

09, 18, 27, 36, 45, and also true for 90, 81, 72, 63, 54.

From the same arrangement too, 234, 567, 8910 are divisible by 9.

and the alternate 135, 468, and the remaining 279 are divisible by 9.

Even if you change the arrangement it is still divisible by 9. What matters is the digits (of course la) such as 567, 765, 675 are divisible by 9.

Then the pattern of three number soon unconciusly sipped into my mind, such as 117, 225, 333, 441, 558, 666, 774, 882, 189, 378, and the rearrangement such as 747, 828 will always caught my attention whenever I saw them.

And I think, about 2 years after that, the rule of 9 changes as it couldn't offers fun for me anymore. The more fun way is how to make a non divisible car plate number to be made divisible.

For example 4566, the result is 3. The pairing of 3 is 6 (because 3+6=9). Therefore 4566 can be made divisible by 9 if it is subtracted with 3 becoming 4563, or added up with 6 becoming 4572. Another example is 3884, the result is 5. The pairing of 5 is 4, hence 3884 is divisible by 9 if it is subtracted with 5 or added up with 4, becoming 3879 and 3888.

And since that, my brain works almost everytime.

The fuse in only a single rule. Introduced briefly by a primary school teacher that taught only at lower level of primary school (darjah satu hingga tiga berada di tahap 1 sekolah rendah).

And that simple rule kept my brain to work more than 10 years non-stop.

The rule too helped me to create my own rule which I called the rule of 3 (I know somebody already discovered this long before me). The rule of 3 is defined as if the sum of the number is divisible by 3, then the whole number is divisible by 3. For example in 498732, 4+9+8+7+3+2=6. 6 is divisible by 3, hence 498732 is divisible by 3.

And so it does happens.

As my brain is summing up the digits, the neurons wired up, creating new dendrites roots channelling each cells building up a big circuit of quick calculator inside my brain.

It was shown up when I was in standard 4 and 5 in Bandar Baru Darulaman Primary School. After each weekly assembly Teacher Naemah, the Penolong Kanan will always assemble the student from standard 4,5 and 6. She hold inside her hand small amout of stationeries from ko-op as gifts to anyone that can answer her question the fastest, which are math question. Not to any surprise, eventhough there are standard 6 students there, I would never leave the assembly empty handed. In the end, on one assembly, eventhough Teacher Naemah didn't taught me in the class and I thought that she didn't knew me, she made an announcement at the beginning saying "Hazrul kamu jangan jawab"

So it does, since the introduction of the rule of number 9, my brain never stop working on math.

And each time I saw a number, the wiring process continues, creating more and more dendrites.

And from the rule of 9, that taught me of reasoning, that taught me on relating everything that I learned in school to the real life, that taught me to practice my knowledge I get in the class to the real world, and also to bring my quest in real world to be put on paper, I learned of maths, and its relation to other knowledge. And of course, that other knowledge is physics, the knowledge of solving everyday's situation into calculation on paper and vice versa. From that too I am more fond to doing experiment, to test my knowledge that I learned from paper. That, later created a bond that never breaks until now, the bond of love between me and chemistry.

A simple rule.

A first level standard 2 primary school teacher.

Introduced when I was only in the second year of my schooling in the government school.

Determines the pattern of wiring inside my brain for the next ten years, and maybe for the rest of my life.

Thanks teacher. Maybe you didn't knew me anymore. I am too can hardly recognizes your face anymore. Eventhough I only remember your first name. Maybe I am just a quite pupil that you didn't noticed in the your school. Maybe I am just one of thousands of the students that you taught. Maybe you thought that with such a salary, you are not significant in other's life. But do know, you are one of the first that wires up somebody's brain.

And thank you to all of my teachers for wiring up my brain.

Sitting in the blue shirt number two in the front row from the left. Picture taken in 1998 while I was in standard 4 in Bandar Baru Darulaman Primary School.

Happy Teachers Day!

p/s: Cikgu Anuar 'kutuk' me when the result of Kuiz Matematik when I was in standard 6 is out, because I only managed to get no. 6 in the 'daerah' after the no.1 belong to a Malay student (from another school) and no. 2,3,4,5 belong to some chinese student haha

4 ulasan:

  1. aku salute cikgu cikgu tersebut....post yg sgt inspiring

  2. "I also found out that ANY NUMBER that is added up to 9 will always result in the same number. For example 4+9=13, in which 1+3=4. And 6+9=15, in which 1+5=6."

    If you add up together 11 with 9;
    11+9=20, 2+0=2, which is not equal to 11.

    However, 2 equals the add-up of 11, which is 1+1=2.

    Therefore, the rule can only be applied to single digit number.

    For double or else digit number, that summation will end up with the summation of the digit, but not the digit itself as u have explained.

    By manipulating algebra and some assimilation with ur discovered rule of 9, I found out many rules of single digit:

    Suppose 'b' is a single digit number then:

    1) for any 'b' added up to 9, the successive digit summation will always end up with b (this is ur rule)

    2) for any 'b' added up to 18, the successive digit summation will always end up with b

    3) for any 'b' added up to 27, the successive digit summation will always end up with b

    In general, any single digit number added up to multiples of 9 will have itself as the result of successive inter-digit summation.

  3. "If you add up together 11 with 9;
    11+9=20, 2+0=2, which is not equal to 11.

    However, 2 equals the add-up of 11, which is 1+1=2.

    Therefore, the rule can only be applied to single digit number"

    Thank you for mentioning about that, I guess one of my biggest problem is in language, that is I can't explain what is in my head easily to other people. Thank you for mentioning that, and that is actually what I mean,

    2+9= 11, 1+1=2
    110+9=119, 1+1+9=11, 1+1=2

    what is in your head is actually what I mean, but I think this is just a small things, just wrong wording

    and moreover this pattern is not only valid to the number that is in base 10, but actually also valid in any base (maybe except for base 2)

    I found this when I was in form 4, learning about base in number

    let say in number that is based 10 (0123456789),

    if the highest number which is 9, is added up to any number, we got the result above,

    if we use let say base 7, (0123456), the highest number which is 6,

    6+4=13, 1+3=4
    6+3=12, 1+2=3

    and other example maybe in base 4, the highest digit is 3

    3+2=11, 1+1=2
    3+3=12, 1+2=3

    beautiful ain't it?

  4. Thats more general a case. Brilliant.