Palindrome Depth

A palindrome is something that is the same forward as backwards -- like mom, dad, race car, I prefer pi, et cetera. Numbers can also be palindromes -- like 141, 88, 1221, et cetera. Now, consider the number 75, 75 is not a palindrome. So, reverse it and add it to itself: 75+57=132. 132 is also not a palindrome, so do it again: 132+231=363. 363 is a palindrome. So, we stop, and we say that 75 is a depth-2 palindrome (because I had to do the process twice to get to a palindrome). Find the palindrome depth of all two-digit numbers.

Source: pg. 97 of Liljedahl, P. (2020). Building Thinking Classrooms in Mathematics Grades K-12: 14 Teaching Practices for Enhancing Learning, Corwin Press.

proposed solution in python

# copy and paste into an online python compiler such as:

# https://www.programiz.com/python-programming/online-compiler/

def isPalindrome(n):

a = str(n)

for i in range(len(a)):

if a[i] != a[len(a)-1-i]:

            return False

return True

def reverse_dig(n):

a = str(n)

b = ""

for i in range(len(a)):

b+= a[len(a)-1-i]

return int(b)

def depth(n):

depth = 0

iterant = n

while (not isPalindrome(iterant)):

print(iterant, "+", reverse_dig(iterant), "=", iterant + reverse_dig(iterant))

iterant += reverse_dig(iterant)

depth += 1

return depth

for n in range(10,100):

print("The depth of ",n," is ",depth(n),"\n")

Name: Patrick Allmann
Position: Math
Email: Send email