Question: This problem involves Discrete Math. A palindrome is a word, number, phrase, or other sequence of characters which reads the same backward as forward, such

This problem involves Discrete Math.

A palindrome is a word, number, phrase, or other sequence of characters which reads the same backward as forward, such as madam or racecar. There are also numeric palindromes, including date/time stamps using short digits 11/11/11 11:11 and long digits 02/02/2020. Sentence-length palindromes ignore capitalization, punctuation, and word boundaries.

PART 1 2021 Unique Palindrome Date

In computer science standard way to represent a date is to convert it to an integer in the form of YYYYMMDD where Y represents a digit of the year,M represents a digit of the month and D represents a digit of the day, always using leading zeros for day and month. For example, May 25th 2021 will be represented as 20200525. Prove, that in 2021 there is only one date which is a palindrome. Show all of your work, include all details, and write clearly and in complete sentences.

PART 2 Short Date Representation Palindrome

A date can also be represented as M/D/YY, e.g. Jan-1-2021 as 1/1/21, Jan-15-2021 as 1/15/21 and Feb-11-2012 as 2/11/12. Note there are no leading zeros in the representation. Prove, that in January 2021, there exactly 11 date representations that are palindrome. Note: ignore the / when determining if the representation is palindrome or not.

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