need help Solution Deciphering

[bjuveges]

[h=2]Problem 11[/h]A palindrome between and is chosen at random. What is the probability that it is divisible by ?

[h=2]Solution[/h]View the palindrome as some number with form (decimal representation): . But because the number is a palindrome, . Recombining this yields . 1001 is divisible by 7, which means that as long as , the palindrome will be divisible by 7. This yields 9 palindromes out of 90 () possibilities for palindromes. However, if , then this gives another case in which the palindrome is divisible by 7. This adds another 9 palindromes to the list, bringing our total to

Basically I only need help in understanding how the answer was found so:

1. How did they get the variables to begin this equation such as a^3,a^2,a^1,a^0 and 10^3,10^2,10?
2. 1001a^3+100a^2? the palindrome part I understand, but how they recombined the values confuses me.
3. a^2=0 & a^2=7 creating different possibilities confuses me.

If anything, I really wanted a better explanation of the problem, using the same method as the solution

 

[mmm4444bot]

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[bjuveges]

Hi there:

All of your threads from yesterday were delayed by the system; I just moved them onto the forum. A delay (up to 24 hours) can result from linking to images at other websites. You can avoid this type of delay, by uploading your images to our server, instead. (See the FAQ.)

Otherwise, you may wait for a moderator to approve such threads.

Cheers :cool:

Ok thanks