I am looking to practice questions like these:
Problem 1 (see text below)
As you can see, these problems involve discrete mathematics, and are sort-of discrete mathematics puzzles. I want to practice more questions like these.
I know that there are multiple books on discrete mathematics, but I have observed that these problems don't test your theoretical knowledge much, but rather your problem-solving skills. Discrete Mathematics books, however, would focus more on the theoretical aspect.
I know that there is a book: Algorithmic Puzzles by Anany and Maria Levitin which seems really good.
Can anyone recommend any other recommendations / books for such problems?
Kind Regards
Canopy
PS: I can not embed images so this is the gist of the first problem in case link doesn't work:
A flexadecimal number consists of a sequence of digits, with the rule that the rightmost digit must be $0$ or $1$, the digit to the left of it is $0$, $1$, or $2$, the third digit (counting from the right) must be at most $3$, and so on. We write flexadecimal numbers in angle brackets to distinguish them from ordinary, decimal numbers. Thus $\langle 34101\rangle$ is a flexadecimal number, but $\langle231\rangle$ is not, because the digit $3$ is too big for its place. (If flexadecimal numbers get very long, we will need ‘digits’ with a value more than $9$.)
Thus, the numbers $1$ to $13$ are represented as$1, 10, 11, 20, 21, 100, 101, 110, 111, 120, 121, 200, 201$ flexadecimal numbers.
(i) Write the numbers from $5$ to $13$ in flexadecimal.
(ii) Describe a workable procedure for converting flexadecimal numbers to decimal, and explain why it works.
(iii) Describe a workable procedure for converting decimal numbers to flexadecimal.
(iv) Describe a procedure for addition that works directly on the digits of two flexadecimal numbers,
(v) Given a flexadecimal number, how could you test whether it is a multiple of $3$ without converting it to decimal?
(vi) If the $\langle100000\rangle$ arrangements of the letters abcdef are listed in alphabetical order and numbered $\langle0\rangle: abcdef , \langle1\rangle: abcdfe, \langle10\rangle: abcedf$, etc., what arrangement appears in position $\langle34101\rangle$ in the list?
Try Project Euler (https://projecteuler.net/about). The problems there are not exclusively discrete, and some require programming, but you will definitely find at least a few discrete puzzles.