1. ## Palindromes -

Hi MHF
Here's my question:
There are 90 four-digit palindromic numbers.
How many of these four-digit palindromic numbers are divisible by 7.
So i have no idea how to start or what to do, i'm unable to obtain a pattern of any sort, i assume there are 10 palindromes between each thousand number bracket (1000-1999, 2000-2999 etc)

2. Originally Posted by 99.95
Hi MHF
Here's my question:
There are 90 four-digit palindromic numbers.
How many of these four-digit palindromic numbers are divisible by 7.
So i have no idea how to start or what to do, i'm unable to obtain a pattern of any sort, i assume there are 10 palindromes between each thousand number bracket (1000-1999, 2000-2999 etc)
Hello 99.95

Yes there are "10 palindromes between each thousand number bracket 1000-1999, 2000-2999 etc"

And also there are only two palindromes in each thousand number bracket for e.g 1001 & 1771, 2002 & 2772,.....9009 & 9779

So in total it makes $\displaystyle 9*2=18$ four-digit palindromic numbers that are divisible by $\displaystyle 7$.

Hope this helps

3. Yes that helps, but i would like to know how you found that there are only two palindromes in each thousand number bracket which are divisble by 7. is there some sort of rule/theorem, or did you happen to use trial and error (Tedious),,
Thanks

4. Originally Posted by 99.95
Yes that helps, but i would like to know how you found that there are only two palindromes in each thousand number bracket which are divisble by 7. is there some sort of rule/theorem, or did you happen to use trial and error (Tedious),,
Thanks
I did it with trial and error for 1000-2000 and than checked to confirm that there are two palindromes in each thousand number!