Saturday, August 10, 2013

Palindromic Numbers

 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.

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