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.
Start with any number. Call it original number
. Reverse the digits of the original number
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
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
Reversing 75 gives 57
Adding 75 and 57 gives 132
Reversing 132 gives 231
Adding 132 and 231 gives 363 and we are done!
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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