In mathematics, a palindrome is a number that reads the same forward and backward. For example, 353 and 787.

By definition, all numbers that have the same digits such as 4, 11, 55, 222, and 6666 are other examples of such number.

Given any numbers, you can use the following simple algorithm to find other palindromes.

Step 1:

Start with any number. Call it original number. Reverse the digits of the original number

Step 2:

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

Step 3:

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

Sound complicated? However, it is not!Let us illustrate

Example #1:


Reversing 75 gives 57

Adding 75 and 57 gives 132

Reversing 132 gives 231

Adding 132 and 231 gives 363 and we are done!

Example #2:


Reversing 255 gives 552

Adding 255 and 552 gives 807

Reversing 807 gives 708

Adding 807 and 708 gives 1515

Reversing 1515 gives 5151

Adding 1515 and 5151 gives 6666. Now we are done!

Now, here is your puzzle. Find 3 numbers less than 100 that require at least 4 additions to obtain palindromes

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