Palindromes are words or numbers that read the same back to front. e.g. ABBA, racecar, 676, 128821, and a recent date 02/02/2020.
Puzzle
Take a positive integer. Reverse the digits to get a new number. Add the two numbers together.
Repeat this process until you get a palindrome.
Some numbers end up in a palindrome quite quickly e.g. 57. 57+75=132, 132+231=363.
Some numbers take a long time – 89 takes an unusually large 24 steps (the most of any number under 10,000 that is known to resolve into a palindrome according to Wikipedia) to reach the palindrome 8,813,200,023,188.
Can you find a starting number that doesn’t end up at a palindrome? Nobody know if this is possible.
You could use this applet that we wrote in maths club to look for one
It is interesting to look for Lychrel numbers in other bases – what happens in binary?