In math, a palindrome is a number that reads the same forward and backward. For example, 353, 787, and 2332 are examples of palindromes. By definition, all numbers that have the same digits such as 4, 11, 55, 222, and 6666 are examples of palindromes.

How to find a palindrome using any given 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 have been 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 the test number is not, use your test number as your original number and repeat the steps above.

Does it sound complicated? However, it is really not that complicated! Let us illustrate with some examples.

Example #1:


Step 1: Reverse the digits of 75.

Reversing 75 gives 57.

Step 2:

Adding 75 and 57 gives 132.

Step 3:

132 is not a palindrome, so repeat the three steps.

Step 1: Reverse the digits of 132.

Reversing 132 gives 231.

Step 2: Add 132 to 231.

After adding 132 and 231 we get 363.

Step 3:

We are done since 363 can read the same backward and forward!

Example #2:


Step 1: Reverse the digits of 255.

Reversing 255 gives 552.

Step 2: Add 255 to 552.

After adding 255 and 552, we get 807.

Step 3:

We are not done since 807 is not a palindrome. Therefore, repeat the three steps.

Step 1: Reverse the digits of 807.

Reversing 807 gives 708.

Step 2: Add 807 to 708.

After adding 807 to 708, we get 1515.

Step 3:

We are not done since 1515 is not a palindrome. Therefore, repeat the three steps.

Step 1: Reverse the digits of 1515.

Reversing 1515 gives 5151.

Step 2: Add 1515 to 5151.

Adding 1515 and 5151 gives 6666.

Now we are done since 6666 is a palindrome!

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

Summary of the steps to find a palindrome

Hopefully, the examples above were easy enough to understand.  See the steps again in the figure below.


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