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What is the smallest five-digit plaindrome that is divisble by $11$?

 

My first thought was $10001$ is this right?

 May 31, 2021
 #1
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10001   isn't  divisible  by  11

 

If  we    assign  alternating  signs  to successive  digits  and  the  sum of the digits  =  0    (or 11), our  number  is divisible  by 11

 

For  example   

121   =   +1  - 2  + 1 =    0   =  divisible by 11

506  =  +5   - 0 +  6   =  11  = divisible by 11

 

The  smallest  I   can find is

 

10901  =   +1   - 0  +   9   - 0  +  1 =    11  =  divisible  by  11

 

 

cool cool cool

 May 31, 2021
edited by CPhill  May 31, 2021
edited by CPhill  May 31, 2021

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