Palindrome Numbers

What is special about the second day of October 2001? It is a palindrome date, it can be written as a number that looks the same written forwards and backwards.

10-02-2001

What does symmetry have to do with palindrome numbers?

Find the five most recent dates that are BEFORE 2 October 2001.

Find the next five FUTURE dates after 2 October 2001.

How can you be sure you have the most recent and the next five?

The number 11 is related to palindrome numbers. Look at the multiplication facts for eleven to determine when this happens. Why does this happen?

An activity for palindrome numbers is to explore the Palindromic Number Conjecture. This conjecture states that any number can be changed into a palindrome number by reversing the digits and adding to the original number a finite amount of times.

For example, the number 23 can be turned into a palindrome in just one step:

23 + 32 => 55

Some numbers take two steps, such as 49:

49 + 94 => 143 + 431 => 484

Using a 100 chart, find and color code all the numbers that are already palindromes. Then color code the one-step palindromes, then color code the two-step palindromes. Continue until each number on the chart is color coded, then observe the patterns made by the different colors. Why does this happen?

Try this experiment with the number 196. What did you find? Mathematicians have tried the reverse and add process for 196 at least nine million times without finding a palindrome. So is 196 an exception? Mathematicians have not been able to prove it either way, that is why it is still an conjecture instead of a theorem.

What about 196?
Some history of palindromes
Palindrome word problems
Word palindromes