These are the show notes for episode 11 of the Travels in a Mathematical World podcast. All palindromic numbers (that is, numbers that remain the same when their digits are reversed) with an even number of digits are divisible by 11. More about the number 11 from Prime Curios. There is a wealth of information on palindromic numbers at worldofnumbers.com.
In the regular Maths History series, Noel-Ann Bradshaw of the University of Greenwich and also Meetings Co-ordinator of the British Society for the History of Mathematics talks about the life of Leonhard Euler. You can read a biography of Euler at the MacTutor History of Mathematics archive. You can find out about Euler’s work at The Euler Archive, including viewing his original papers.
Since this is the last episode until next year, I also proposed a little Christmas puzzle based on this episode’s episode number result on palindromic numbers. You can make palindromic numbers by taking a number, reversing its digits and adding these two numbers together, then repeating until you get a palindromic number. For example, take 92. Add 92 to 29 and you get 121, which is a palindrome. Some numbers need more than one step. For example, take 94. Add this to 49 and you get 143. Add this to 341 and you get 484, which is a palindrome. Try it: How many steps does it take for each of the rest of the nineties, 95-99? Try it for other numbers, although I wouldn’t recommend trying it for 196. You can find out the answer to this question and why not to try 196 by reading a question at the Math Forum, “Making Numbers into Palindromic Numbers”.