This article is about a number that has some truly exceptional properties. That number is **1089**

**Most Amusing Property of 1089**

Select a three digit number (where the units and hundreds digits are not the same) and follow these instructions:

Step 1: Choose any three-digit number (where the units and hundreds digits are not the same).

Let us randomly select the number 469

Step 2: Reverse the digits of the number you have selected

So reverse of 469 is 964

Step 3: Subtract the smaller number from the bigger one

964 – 469 = 495

Step 4: Once again reverse the digits of this difference

Reverse of 495 is 594

Step 5: Add the last two numbers

594+495 = 1089

This result will be the same for any 3-digit number chosen in step 1. Isn’t it astonishing that regardless of which number you select at the beginning, you will get 1089 as the result. Check out similar amusing property of 6174, which is also called Kaprekar Constant, named after Indian recreational mathematician D.R.Kaprekar.

**Another Interesting property of 1089**

Let’s look at the first nine multiples of 1,089:

1089 x 1 = 1089

1089 x 2 = 2178

1089 x 3 = 3267

1089 x 4 = 4356

1089 x 5 = 5445

1089 x 6 = 6534

1089 x 7 = 7623

1089 x 8 = 8712

1089 x 9 = 9801

I am sure you notice a pattern in the products. Look at the first and ninth products. They are the reverses of one another. The second and the eighth are also reverses of one another. And so the pattern continues, until the fifth product is the reverse of itself, known as a palindromic number

**One More Unique Property of 1089**

33^2 = 1089 = 65^2 – 56^2

The above representation is also unique among two digit numbers.

Do you agree that there is a particular beauty in the number 1089?

Try with 384 you will not get 1089

Similar but slightly different magic you have in number 72, which in financial economics is called Rule of 72 . If you know the the rate of interest , say r then dividing 72 by r gives the number of years required to double your principal amount. Likewise if you want money to be doubled over a certain period ,say t, then dividing 72 by t gives the required rate of interest Here, . Compouding of principal by interest rate is annual .

Hi Sharad,

I’m truly glad that you pointed out property or rule of 72 in this context. In one of my earlier posts I’ve discussed this in details – http://www.quickermaths.com/rule-of-72-estimation-of-compound-interest-and-time/

Regards,

Vineet