Reverse Add Rule for finding Palindromes

Given any number, 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




I told the children that they can be playfully “evil mathematicians” if they teach someone how easy it is to reverse add to find a palindrome and then gave that person a Lychrel number like 196 or 295 which they would never be able to solve.


K-2nd grade I simply want them to do one step reverse add palindromes because they would not have to carry to the next place value. All 2+ step reverse add palindromes require carrying the tens value to the next column in the addition problem. For many of my 2-4th graders they were learning vertical addition with carrying for the first time with me. This will take weeks to master but we will stay at it. They should practice a lot so it becomes second nature.


3-7th graders can solve any multi-step palindrome up to 24 on the pdf.


For my 4-7th graders, I challenged them to LIST AS MANY PRIME PALINDROMES AS YOU CAN: __________________________________________

Note: Prime numbers must have only two distinct (different) factors, 1 and the prime number itself.



There are five types of square palindromes:

1. One-digit squares: _______ ________ ________

2. Sequences of 2, 3, 4 ...-digit numbers that are squared to palindromes (can you find a pattern?):

11^2 = 121

101^2 = 10,201

1001^2 = 

10001^2 =

1000000001^2 =

22^2 = 

202^2 = 

2002^2 = 

20002^2 =

2000000002^2 =

3. Numbers with multiple 1s squared (how many are there?)

11^2 = 121

111^2 =   



See the answer keys on the pdfs. Have fun.

Palindromes_K-3.pdf2.03 MB
Palindromes_Reverse_Add_and_Squares_4-7th_Grade.pdf2.4 MB