Lesson: The Fundamental Counting Principle

Comment on The Fundamental Counting Principle

Question at http://gmatclub.com/forum/a-palindromic-number-reads-the-same-forward-and-backward-214196.html is not clear to me. Could you please help me on this?

How many 6-digits number are Palindromic numbers? A Palindromic number reads the same forward and backward, example 12121.
A) 100
B) 610
C) 729
D) 900
E) 1000
gmat-admin's picture

I'm not a huge fan of that question because it first starts by talking about 6-digit numbers and then gives an example of a 5-digit number that works. However, my solution appears on that same page.
The basic idea is that, once we have selected the first 3 digits of the number, the last 3 digits automatically follow.
For example, if the first 3 digits are 356---, then (to be a palindrome), the last 3 digits must be ---652, so we get the number 356652.
Likewise, if the first 3 digits are 197---, then (to be a palindrome), the last 3 digits must be ---791, so we get the number 197791.

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