A number like 12321 is a 'palindrome' because it reads the same backwards as forwards. A friend of mine claims that all palindromes with 4 digits are exactly divisible by 11. Is he right? Explain yourselves, or face the terror of no medal! (from Thinking Mathematically, page 4 by John Mason).

Question

anonymous · Answer

your friend is right - i cant explain why. Its something i read in a math puzzle book.

anonymous · Answer

yes it is correct..................as ever number in four digit starts with the same number and ends with the same and this general pattern make it divisable by 11

anonymous · Answer

The two middle numbers have to play a part as well/

anonymous · Answer

Your answer is incomplete!

anonymous · Answer

Hint: What is the general form of a 4 digit palindromic number?

anonymous · Answer

its abba

anonymous · Answer

And what is 'abba' made up of?

anonymous · Answer

abba as a number is:
$$1000a+100b+10b+a \Longrightarrow 1001a+110b \Longrightarrow 11(91a+10b)$$
So it is always divisible by 11.

anonymous · Answer

Points to joe!