Palindromes mod 11

There are several palindromes which are divisible by 11:

1 \color{magenta} 1 4 \color{#CEBB00} 4 7 \color{cyan} 7 7 \color{cyan} 7 4 \color{#CEBB00} 4 1 \color{magenta} 1 \equiv 0 0 ( 11 ) (11)

8 \color{magenta} 8 2 \color{#CEBB00} 2 3 \color{cyan} 3 3 \color{cyan} 3 2 \color{#CEBB00} 2 8 \color{magenta} 8 \equiv 0 0 ( 11 ) (11)

How many 6 digits palindromes are not divisible by 11?

Clarification: A palindrome is a number that can be read from right to left as well as from left to right


The answer is 0.

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1 solution

X X
Jul 26, 2018

If a 6-digit palindrome is in the form of a b c c b a \overline{abccba} ( a , b , c a,b,c are not nessecarily distinct),then it equals 100001 a + 10010 b + 1100 c = 11 ( 9091 a + 910 b + 100 c ) 100001a+10010b+1100c=11(9091a+910b+100c) which is always a multiple of 11.

are u home-schooled or u take extra classes? your parents proly planning to send you to Harvard. And you would be labeled the genus forever :)

A Former Brilliant Member - 2 years, 10 months ago

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I learned math myself because it's interesting.By the way,why would you say that I'm a genus?

X X - 2 years, 10 months ago

I was tricked by the problem.

Naren Bhandari - 2 years, 10 months ago

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How did it trick you?(But you still got it right.)

X X - 2 years, 10 months ago

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I mean in my first attempt I read it as, " how many 6 digits palindromes are divisible by 11?". Later on i read the problem it is very clear that we are supposed to answer; how many are not ?".

Naren Bhandari - 2 years, 10 months ago

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@Naren Bhandari Oh,I see.Have to be careful.

X X - 2 years, 10 months ago

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