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:

\ counting change (SICP section 1.2.2)

: table create does> swap cells + @ ;
table coin-value 0 , 1 , 5 , 10 , 25 , 50 ,

: count-change ( total coin -- n )
  over 0= if
    2drop 1
  else over 0< over 0= or if
    2drop 0
  else
    2dup coin-value - over recurse
    >r 1- recurse r> +
  then then ;

100 5 count-change .