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?