Figures!! The thing that most interested me right from my school days and even now it is interesting me. Hey, dont mistake figures for babes, but it is all about digits. I like playing with figures and I observed one peculiar property of palindrome numbers, during my school days. Actually, I observed it during my college days. As you know I am currently in a place where colleges are called as schools,
I am using the same notation ;-), when you are in rome, become roman :-P.
Coming to the matter, this is what I observed: A palindrome integer of even length will always be a multiple of 11. If it sounds obvious to you or you dont like playing with figures, then press the "X" button on the right-top corner.
11, 1221, 1441... are some examples of even-lengthed palindrome numbers. A number is a multiple of 11, if the difference between the sum of the digits at even position and the sum of digits at odd position is a multiple of 11 or 0. Take 385 for example, (3+5)-8 is zero, hence multiple of 11.
Now, let us see palindrome numbers. If the number of digits is odd, then the number of digits at odd position will be more than that of even position, and also "odd digit set", and "even digit set" will be with unequal digits, hence it cannot be a multiple of 11. In even length case, the digits at odd positions will be same as the digits at even positions. so the difference will be zero and hence it will be multiple of 11.
4 comments:
kalai: hmm.
nice finding there.. reminds me of my school days where we a group of friends thought of patenting all the stuff with numbers which we founs/did for timepass.. :D
dai .. un theramaikku ellai illaiya ?
i remember u telling me something else like this before . but i dont rem wht u said .
sudha: thanks!, we cannot patent
all these, some geek would have
done it before :-(
jagan: machi, nalla naan sonna
maathiriye comment pannirukke. koodiya seekrathule, naanum Un
blogle oru nalla comment podren. Hear is the deal !!
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