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- 99,999 - 10,000 + 1 = 90,000
- Therefore, there are 90,000 five-digit numbers.
Pretty Palindromic Patterns
Palindromic numbers are numbers that read the same forward and backward. For example,
numbers like 66, 848, 575, 797, and 1111 are all palindromes because they look the same
whether you read them from left to right or right to left.
Creating 3-Digit Palindromes
Let’s explore how to create all possible 3-digit palindromes using the digits 1, 2, and 3. A 3-digit
palindrome has the same first and third digits. Here’s how they look:
121: The first and last digits are 1, and the middle digit is 2.
131: The first and last digits are 1, and the middle digit is 3.
212: The first and last digits are 2, and the middle digit is 1.
232: The first and last digits are 2, and the middle digit is 3.
313: The first and last digits are 3, and the middle digit is 1.
323: The first and last digits are 3, and the middle digit is 2.
These are all the possible 3-digit palindromes you can create using only the digits 1, 2, and 3.
Reverse-and-Add Palindromes
Now, let’s explore a fun activity involving palindromes, called the Reverse-and-Add method.
Here’s how it works:
Start with a 2-digit number. For example, let’s pick 34.
Reverse the digits of the number: 34 becomes 43.
Add the original number to its reverse: 34 + 43 = 77
Check if the result is a palindrome. If it is, you’re done. If not, reverse the new number and add
again.
Let’s try another example with a different number, 47:
Reverse 47 to get 74.
Add them: 47 + 74 = 121.
Since 121 is a palindrome, we stop here.
Let’s try with 89:
Reverse 89 to get 98.
Add them: 89 + 98 = 187 (not a palindrome, so continue).
Reverse 187 to get 781.
Add them: 187 + 781 = 968 (not a palindrome, so continue).
Reverse 968 to get 869.
Add them: 968 + 869 = 1837 (still not a palindrome).
In this case, you would keep repeating the process until you get a palindrome. Some numbers
take several steps to become a palindrome, while others might never reach one!
