Tuesday, 12 August 2008

Use of Algebra | Explaining The Mysterious Answer 22

What is the use of algebra?

It is the basis of math learning.

It forms the foundation where more advanced learning is piled onto. It also serves to explain numerous questions.

One of the exciting question is shown below. It involves the explanation of a tricky problem involving the mysterious number 22.

Question / Steps:

  1. Choose any 3-digit number.

  2. All the digit cannot be repeated.

  3. Form all possible 2-digit numbers out of the chosen 3-digit number.

  4. Add up all these 2-digit numbers.

  5. Also add up the individual digits of the chosen 3-digit number.

  6. Finally divide the sum of the 2-digit numbers with the sum of the individual 3-digit number.

The answer will be 22 no matter what the chosen number is.

Let choose a 3-digit number of 123.
Forming all the 2-digit numbers: 12, 13, 23, 21, 31, 32
Adding up the above 2-digit numbers: 132
Adding up the individual 3-digit number: 1 + 2 + 3 = 6
Dividing the above 2 resultants: 132 / 6 = 22.

How do we explain it?

Use our famous algebra!

We start the analysis by letting the chosen number be xyz ( to be generic).

This number can be written as 100x + 10y + z. <== This is application of algebra.

Adding up all the possible 2-digit numbers that can be formed means the below:
(10x + y) + (10x + Z) + (10y + z) + (10y + x) + (10z + x) + (10z + y)
= 22x + 22y + 22z = 22(x + y + z)

Next, if we add up the individual digit of the 3-digit chosen number, (x + y + z).

Dividing the 2 resultants, we get 22(x + y + z) / ( x + y + z) ==> 22.

From the example of above, it can shown clearly how useful is algebra in explaining the principle of obtaining the answer 22. Simple isn't it.

That's the beauty of math, don't you agree?

Should we have a beauty contest for the mathematical symbols?

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