There are four types of common coins in   US   currency:

   quarters   (25 cents)
   dimes   (10 cents)
   nickels   (5 cents),   and 
   pennies   (1 cent) 


There are six ways to make change for 15 cents:

   A dime and a nickel 
   A dime and 5 pennies
   3 nickels
   2 nickels and 5 pennies
   A nickel and 10 pennies
   15 pennies


Task

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



Optional

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).



References

 an algorithm from the book Structure and Interpretation of Computer Programs.
 an article in the algorithmist.
 Change-making problem on Wikipedia.


amount=100;
coins=[25 10 5 1];
n_coins=zeros(coins);
ways=0;
 
for a=0:4
    for b=0:10
        for c=0:20
            for d=0:100
                n_coins=[a b c d];
                change=sum(n_coins.*coins);
                if change==amount then
                    ways=ways+1;
                elseif change>amount
                    break
                end
            end
        end
    end
end
 
disp(ways);