**In Mathematics, Palindrome is the number that reads the same forward and backward. For example, 111,252,7007 are all palindromic numbers.****Method to find Palindromic Numbers :**

Start with any number. Call it

**original number**. Reverse the digits of the original number

original number = 436

Call the number whose digits are reversed

**new number**. Add the new number to your original number.

Call the number found by adding the new number to the original number

**test number**

new number = 634

**test number = new number + original number**

test number = 634 + 436 = 1070

If test number is a palindrome, you are done. If not, use your test number as your original number and repeat the steps above

original number = 1070

new number = 0701

test number = 1070 + 0701 = 1771

Source : http://www.basic-mathematics.com/palindrome.html

**Find 3 numbers less than 100 that require at least 4 additions to obtain palindromes**

1.

**Number : 69**

Addition: 1

Original number = 69

new number = 96

test number = 165

Addition: 2

original number = 165

new number = 561

test number = 726

Addition: 3

original number = 726

new number = 627

test number = 1353

Addition: 4

original number = 1353

new number = 3531

test number = 4884

**4884, which is a palindrome.**

2.

**Number : 78**

Addition : 1

original number = 78

new number = 87

test number = 165

Addition : 2

original number = 165

new number = 561

test number = 726

Addition : 3

original number = 726

new number = 627

test number = 1353

Addition : 4

original number = 1353

new number = 3531

test number = 4884

**4884, which is a palindrome.**

3.

**Number : 79**

Addition : 1

original number = 79

new number = 97

test number = 176

Addition : 2

original number = 176

new number = 671

test number = 847

Addition : 3

original number = 847

new number = 748

test number = 1595

Addition :4

original number = 1595

new number = 5951

test number = 7546

Addition : 5

original number = 7546

new number = 6457

test number =14,003

Addition : 6

original number = 14,003

new number = 30,041

test number = 44,044

**44,044, which is a palindrome.**