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.
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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