# Elven mystical numbers

**Discrete Mathematics**Level 5

Before the problem itself, it would be a good idea to explain what an "Elven mystical number" is (**EMN** in the further text). Each **EMN** has the following properties:

(1) Number of digits is odd

(2) The middle digit is the peak and it is the greatest digit in number, also it appears only once

(3) Going from the peak to one of the ends, numbers decrease or stay the same

(4) These numbers are also palindromes

Now, when the **EMN** is not so mystical, the question is, how many 11-digit **EMN**s exist?

**Details and assumptions:**

Middle digit is at the same "distance" from left and right end, so in 5-digit number, middle digit is the \( 3^{rd} \) one.

Example of

**EMN**s: 12321, 7778777, 111575111, ...Example of non-

**EMN**s: 11111 (rule (2)), 123321 (rule (1) and (2)), 1325231 (rule (3)), 1237521 (rule (4))If we have 11-digit number, whose first digit is null, then we actually don't have an 11-digit number.

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