Miscellaneous Problems

Problem 1. The names of the whole numbers from one to twelve are written down in lexicographical order, that is, in the order in which they appear in the dictionary. What is the fourth number on the list?

Problem 2. In the Microsoft software Excel, columns are labelled by letters. The first twenty six columns are labelled A through Z, the twenty seventh is labelled AA, the twenty eighth AB, etc. What label appears on the 2023th column?

Problem 3. How many (decimal) whole numbers are there between 1 and 1000 whose digits add up to 12?

A palindrome is a natural number whose decimal expansion is symmetric, that is, it reads the same backwards as forwards. For example, 1, 11, 345543, are all palindromes.

Problem 4. If the sequence of palindromes is written in ascending order 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, . . . , 99, 101, 111, 121, . . . , which palindrome follows 1991?

Problem 5. The palindrome 10001 is strictly between two other palindromes. Which two?

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