### Brain Teasers

# Palindrome

What is the only non-palindromic integer whose cube is a palindrome?

### Hint

A palindrome is a number that reads the same forward as it does backward. An example would be 1221. An integer is a number that has no decimal places. A cube is the result of multiplying a number by itself three times.### Answer

22012201^3 = 10662526601

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## Comments

Is there a way to figure this out without just running through numbers until you get the answer? My calculator's worn out.

This was a math problem once asked during one of my math classes. The professor didn't provide a solution, it was more as if he was stating a fact. I think he got if from a math trivia book or something.

great teaser!

i would have never gotten that!!

How can we verify that this is the only one? Do we just take your word for it? This rather belongs in the trivia category, unless you can back up the answer with some Mtahematical reasoning.

oops...Mathematical...

Jan 07, 2004

I do not mean to criticize your teaser, but I agree with Bob and Jim. Sitting around and trying numbers is not the best way, unless one is perhaps obsessive-compulsive. I, too, am curious to know if there is a better way to come to this answer.

How about 7 would you consider that a palindrome? And 7 cubed= 343.

11 cubed=1331.

oops scratch that last one.

7 reads the same forwards as it does backwards.

This teaser is good, but you need to say that it is the only known number like it. There are still a lot of numbers noone has ever checked.

that went way over my head

To calculate this easier, use something like excel, and copy he fomula. Pretty easy. Good One.

Or write a simple Basic program.

here we go again, does it make you feel smart to ask these impossible questions? you don't even know how to get the answer, so how do we? i could look up impossible stuff in textbooks no one ever reads and ask you about it, but i'd rather be fair, fun, and realistic.

I wrote a BASIC program on my TI-84+ SE that checked numbers up to about 250,000 before the battery ran out and the ram got cleared. The only anser it got was 2201. I might rewrite it or just write it on the computer in C.

thats not a very good hint

if you dont know what a cube is, a nd you dont know what a palindrome is, then you are very likely not going to get this teaser.

if you dont know what a cube is, a nd you dont know what a palindrome is, then you are very likely not going to get this teaser.

I have verified up to 5,000,000.

I am working on a verification up to 1,000,000,000. I will post results when complete.

I am working on a verification up to 1,000,000,000. I will post results when complete.

Sep 27, 2007

this question sucks balls.

Sep 27, 2007

fat balls

How to validate it's the only one non-palindromic?

It is interesting trivia, but I was expecting an explanation of why this has to be the ONLY integer with this property.

my goodness ....how do u get such answers ...???

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