Problem Statement

There are four types of common coins in   US   currency:

There are six ways to make change for 15 cents:

How many ways are there to make change for a dollar using these common coins?     (1 dollar = 100 cents).

Less common are dollar coins (100 cents);   and very rare are half dollars (50 cents).   With the addition of these two coins, how many ways are there to make change for $1000? (Note:   the answer is larger than   232).

Let's start with the solution:

program count_the_coins;
    print(count([1, 5, 10, 25], 100));
    print(count([1, 5, 10, 25, 50, 100], 1000 * 100));

    proc count(coins, n);
        tab := {[0, 1]};
        loop for coin in coins do
            loop for i in [coin..n] do
                tab(i) +:= tab(i - coin) ? 0;
            end loop;
        end loop;
        return tab(n);
    end proc;
end program;