Interesting properties of 11

There are three interesting facts about 11 that you 're going to see -


I. If n is smaller than 5 then 11 ^ n will be a palindromic number meaning it can be read the same backwards as forwards

1. 11 ^ 1 = 11
2. 11 ^ 2 = 121
3. 11 ^ 3 = 1331
4. 11 ^ 4 = 14641

II. To multiply 2-digit numbers by 11 is simple : Just add the 2 digits and place the result in the middle eg:-

1. 11 * 11 = 121 The 2 is darkened to show that it is achieved from adding 1 and 1.

If the  sum of the 2 digits is more than 10 then the extra 1 is added to the tens place eg:-

1. 47 * 11 = 5 1 7 . The 1 is from the ones place of 11 ( 4 + 7 ) and the 5 is from adding the 1 from the tens place of eleven . 

III . 11 ^ n also appears in Pascal 's Triangle invented by Blaise Pascal which is used to calculate
probability

1. 11 = 11^1
2. 121 = 11^2
3. 1331 = 11^3
4. 14641 = 11^4
5. 161051 = 11^5
6. 1771561 = 11^6
7. 19487171 = 11^7

 And to calculate probability the numbers in a horizontal line must be added up.