FLPoTD: Writing Checks

This problem was inspired by a puzzle on the 2021 Mystery Hunt:

Given a string S of characters from the latin alphabet (a-z), find the smallest nonnegative amount (dollars and cents) whose spelled-out representation contains S as a subsequence.

• The dollar amount should not include 'and': 123 is "one hundred twenty three", not "one hundred and twenty three".
• If the amount is less than $1.00 (one dollar and zero cents), then the dollar amount is omitted: $0.46 is "forty six cents"
• The cents is always expressed: $46.00 is "forty six dollars and zero cents"
• This table contains the names of powers of 10: https://en.wikipedia.org/wiki/Power_of_10#Positive_powers

Follow-up:

• Given a list of strings, all of which use exclusively lowercase letters, find the most expensive word.

A Number Theory Appetizer

Fix $x, y \in N$ such that $x$ and $y$ are coprime. Prove that there exists $n \in N$ such that $k | x^n - y^n$ for any $k \in N$.

A C puzzle

Consider the following C code:

#include <stdio.h>

enum bitmask
{
    bitmask_A = 1,
    bitmask_B = 2,
    bitmask_C = 4
};
typedef enum bitmask bitmask;

struct a_s
{
    bitmask member;
};
typedef struct a_s a_t;

bitmask
f(a_t *arg)
{
    arg->member |= bitmask_B;
    return bitmask_C;
}

int
main()
{
    a_t foo;
    foo.member = bitmask_A;
    foo.member |= f(&foo);
    printf("%d\n", foo.member);
    return 0;
}

What happens?

A Silly Physics Problem

Brought to you by Tyler Christensen

If you have two ideal 1F capacitors, one at 0V and one at 10V, and you connect them together instantaneously with an ideal superconductor, what is the final voltage? Note all components have zero physical size and there is zero parasitic inductance.